Shadow Play Game Integration

Let me analyze the task. I need to create a brand new game that hasn't been done before. The last game was "Harmonograph" - a mathematical art puzzle. I need to make something different.

Let me first check what games already exist in the /space/games/ directory to avoid duplication, then brainstorm and create a new, unique game.

Let me install the shell tools and space skills tools to get started.

Let me see the full list of games and understand what's been done. There are a LOT of games here. Let me think about what kind of game would be unique and interesting.

Looking at the existing games:

• 2048, abyssal-descent, aether-spire, alchemy-lab, battleship, beat-drop, biome-builder, block-cascade, bonsai-zen, box-pusher, bridge-lab, chroma-shift, cipher-master, circuit-breaker, clockwork, code-quest, color-clash, constellation-cartographer, conveyor-sort, cosmic-forge, deep-cast, dna-sequencer, dot-dash, dungeon-deck, dungeon-delver, echo-maze, forge-master, gear-works, gem-cascade, gravity-golf, gravity-wells, gridlock, harmonograph, harmony-grid, hashi, hive, inkflow, knot-free, lighthouse-keeper, logic-lab, loop-lab, lumen, lunar-lander, magnetar, mancala, mastermind, math-blitz, mine-sweeper, murmuration, mycelium, neon-breakout, neon-flip, neon-flow, nexus-defense, nova-pop, orbit-weaver, paper-wings, photon-path, picross-quest, pixel-painter, powder-lab, prism, pulse, pyrotechnia, quantum-circuit, reaction-chain, realm-guard, reef-keeper, safecracker, sizzle, snake, sonar-echo, stained-glass-studio, starweave, stellar-pinball, stock-tycoon, sudoku-sage, synapse, tangram-quest, terraform, tide-pool, tower-of-hanoi, transit-link, tumbler, type-storm, vial-sort, word-forge, word-hunt

That's a huge collection. Let me think about what's NOT here:

Genres covered:

• Puzzle: picross, sudoku, hashi, tangram, knot-free, etc.
• Action: snake, breakout, pinball, etc.
• Strategy: battleship, mancala, tower defense, etc.
• Rhythm: beat-drop, pulse, etc.
• Art/Creative: pixel-painter, harmonograph, stained-glass, inkflow, etc.
• Physics: gravity-golf, lunar-lander, etc.
• Logic: mastermind, circuit-breaker, etc.
• Word: word-forge, word-hunt, type-storm, code-quest
• Simulation: stock-tycoon, biome-builder, terraform, etc.
• Card/Board: dungeon-deck, etc.

What's missing? Let me think of something unique...

Ideas:

1. Origami/Folding puzzle - fold paper to match shapes
2. Lockpicking game - rotate pins/tumblers (safecracker might be similar)
3. Glassblowing - shape molten glass by blowing and rotating
4. Topography/Contour map - draw contour lines on a landscape
5. Seismograph - read seismic waves to locate earthquake epicenters
6. Astrolabe/Celestial navigation - use stars to navigate
7. Calligraphy - trace strokes with proper brush pressure
8. Knot tying - interactive knot tying puzzle
9. Weaving/Loom - create patterns on a loom
10. Theremin - play music by hand position
11. Shadow puppetry - arrange objects to cast shadow shapes
12. Ice carving - carve ice blocks
13. Marble run - design marble tracks
14. Periscope - navigate submarine using periscope
15. Weather station - predict weather from instruments
16. Cartographer - map unexplored terrain
17. Semaphore/Flag signaling - communicate with flags
18. Morse code - send/receive morse (dot-dash might cover this)
19. Juggling - keep balls in the air
20. Tightrope walker - balance game
21. Glass harmonica - play a glass harmonica
22. Conveyor/Factory - conveyor-sort exists
23. Blacksmith - forge-master exists
24. Pottery wheel - shape clay on a spinning wheel
25. Enigma machine - cipher-master might cover ciphers
26. Slide puzzle - classic 15-puzzle
27. Nonogram - picross-quest covers this
28. Sokoban - box-pusher covers this
29. Pipe/Plumbing - connect pipes
30. Electrical circuit - circuit-breaker, quantum-circuit cover this
31. Optics/Laser - photon-path covers this
32. Music sequencer - harmony-grid, pulse cover music
33. Fishing - deep-cast covers this
34. Gardening - mycelium, reef-keeper, bonsai-zen cover nature
35. Cooking - sizzle covers cooking
36. Chemistry - alchemy-lab, powder-lab, vial-sort cover chemistry
37. DNA - dna-sequencer covers this
38. Space - many space games
39. Tower defense - nexus-defense, realm-guard
40. Idle/incremental - stock-tycoon
41. Sorting - conveyor-sort, vial-sort
42. Maze - echo-maze
43. Memory - neon-flip
44. Typing - type-storm, code-quest
45. Word - word-forge, word-hunt

Let me think more creatively about what's truly unique...

Shadow Puppet Theater - This is really interesting! Players arrange 2D shapes (hands, objects) in front of a light source to cast shadows that match target silhouettes on a wall. The shadow changes based on the distance from the light, the angle, and the shape. This combines spatial reasoning, physics of light/shadow, and creativity.

Origami Folding - A step-by-step paper folding puzzle where you fold a square of paper to create different shapes. Each fold is a line across the paper, and the paper folds over. This is mechanically unique and visually interesting.

Pottery Wheel - Shape clay on a spinning wheel by controlling pressure and position. The clay deforms based on where you apply pressure. You need to match target profiles. This is a relaxing, creative game with a unique mechanic.

Marble Maze / Labyrinth - Tilt a board to guide a marble through a maze avoiding holes. This uses device tilt or mouse drag to tilt. Classic but not in the list.

Calligraphy / Brush Strokes - Trace characters or shapes with proper brush pressure, speed, and angle. The quality of your stroke is evaluated.

Weaving Loom - Create textile patterns by threading a loom. You choose warp and weft colors and patterns to match target designs.

Glassblowing - Shape molten glass by controlling breath (air pressure) and rotation. The glass expands and deforms based on these inputs.

Topography Builder - Raise and lower terrain to create a landscape that matches a target contour map. Water flows based on the terrain.

Shadow Puppet seems really unique and visually striking. Let me think about this more...

Actually, let me think about what would be:

1. Mechanically unique
2. Visually impressive
3. Engaging for more than 2 minutes
4. Educational or useful

Origami Folding Puzzle - This is very unique. The mechanic of folding paper is not represented in any existing game. It's educational (teaches origami), visually interesting (paper folding animations), and has puzzle depth (multiple folds, matching targets).

Let me think about how to implement this:

• Start with a square paper
• Player draws a fold line (or selects from predefined fold lines)
• The paper folds along that line
• After multiple folds, the paper should match a target shape
• Could have levels with increasing complexity

Actually, implementing realistic paper folding in 2D canvas is quite complex. The math behind paper folding (origami mathematics) is non-trivial.

Let me think of something more feasible but still unique...

Shadow Puppet Theater - This could work well:

• A light source on one side
• Objects/shapes that can be positioned and rotated
• The shadow is cast on the opposite wall
• Player needs to arrange objects so the shadow matches a target silhouette
• Distance from light affects shadow size
• Angle affects shadow shape
• Multiple objects can overlap to create complex shadows

This is mechanically unique, visually striking, and has puzzle depth. Let me go with this!

Actually, wait. Let me think about another idea:

Constellation/Star Map - constellation-cartographer already exists.

Theremin - A musical instrument game where you control pitch and volume with mouse position. Could be interesting but might be too simple.

Lockpicking - safecracker might be similar.

Periscope/Submarine - Navigate using a periscope, identify ships, etc.

Weather Forecaster - Read weather instruments (barometer, anemometer, etc.) and predict weather. Educational and unique.

Seismograph - Analyze seismic waves to locate earthquake epicenters. Educational and unique.

Astrolabe - Use an astrolabe to determine position from stars. Educational and unique.

Let me go with something that's both fun and educational.

Shadow Puppet Theater is my top choice. It's:

• Visually unique (warm light, shadows, silhouettes)
• Mechanically unique (manipulating light and shadow)
• Educational (teaches about light, shadow, perspective)
• Has puzzle depth (multiple objects, angles, distances)
• Relaxing and creative

Let me design this game:

Concept: "Shadow Play" - You're a shadow puppeteer. Arrange cutout shapes in front of a light to cast shadows that match target silhouettes on a screen.

Mechanics:

• A light source on the left
• A screen/wall on the right
• Cutout shapes (animals, objects, geometric shapes) that you can drag, rotate, and move closer/farther from the light
• The shadow on the wall changes based on:
  • Distance from light (closer = bigger shadow)
  • Rotation (changes the projected shape)
  • Position (affects where shadow appears)
• Multiple shapes can be combined to create complex shadows
• Target silhouettes to match (e.g., a rabbit, a bird, a castle)

Levels:

1. Simple: One shape, match a basic silhouette
2. Medium: Two shapes, combine to make a composite shadow
3. Hard: Multiple shapes, precise positioning needed

Visual Style:

• Warm, theatrical lighting
• Dark background with a glowing screen
• Paper cutout aesthetic for the shapes
• Soft, realistic shadow rendering

Scoring: How closely the shadow matches the target silhouette (pixel comparison)

Actually, implementing realistic shadow projection with proper light physics in canvas is doable but complex. Let me think about the implementation:

1. Light source at position (lx, ly)
2. Object at position (ox, oy) with rotation θ
3. Screen at distance D from light
4. Shadow position on screen: project the object's vertices from the light source onto the screen
5. Shadow scale: proportional to (D - distance_from_light) / distance_from_light... actually, the shadow gets bigger when the object is closer to the light and farther from the screen.

The math:

• Light at position L
• Object vertex at position P
• Screen is a vertical line at x = screenX
• Shadow point S = L + (P - L) * (screenX - L.x) / (P.x - L.x)

This is perspective projection. The shadow is the projection of the object's silhouette onto the screen plane from the light source.

For 2D, if the light is at (lx, ly) and the screen is a vertical line at x = sx:

• For each vertex (vx, vy) of the object:
  • shadow_x = sx
  • shadow_y = ly + (vy - ly) * (sx - lx) / (vx - lx)

The shadow is the polygon formed by these projected vertices.

This is actually quite elegant and implementable! Let me go with this.

Wait, but I need to think about what makes this a game vs just a toy. The puzzle aspect is matching target silhouettes. Let me think about how to score:

1. Render the player's shadow to an offscreen canvas
2. Render the target silhouette
3. Compare pixel by pixel (IoU - Intersection over Union)
4. Score based on similarity

This is a solid game design. Let me implement it!

Actually, let me reconsider. The shadow projection in 2D top-down view might be confusing. Let me think about the view:

Option A: Top-down view - light on left, screen on right, objects in between. Shadows project horizontally. This is like looking down at a stage from above.

Option B: Side view - we see the screen from the front, with the light behind the objects. The shadow appears on the screen. We see the objects in profile.

Option C: 3D-ish perspective view - we see the stage from the audience perspective.

I think Option A (top-down) is the most intuitive for a puzzle game. The player can see:

• The light source (left)
• The objects (middle, draggable)
• The screen (right, showing the shadow)
• The target silhouette (overlaid on or next to the screen)

Let me design the UI:

• Left side: Light source (glowing circle)
• Middle: Play area where objects can be dragged, rotated, moved
• Right side: Screen showing the projected shadow + target outline
• Bottom: Object palette (shapes to add to the stage)
• Top: Level info, score, controls

Actually, for a cleaner design, let me think about this differently.

Let me reconsider the whole concept. Maybe instead of a physics-based shadow projection, I should think about what's simpler to implement but still unique and fun.

Origami is still my top pick for uniqueness. Let me think about a simplified origami implementation:

• Paper is a square represented as a polygon (list of vertices)
• A fold is defined by a line (two points)
• When you fold, the paper on one side of the line is reflected across the line
• The paper's shape updates to the new polygon
• After N folds, compare with target shape

This is actually very doable! The key operation is:

1. Define a fold line
2. Split the paper polygon by the line
3. Reflect one part across the line
4. The new shape is the union of the unreflected part and the reflected part

Wait, actually in origami, when you fold, the paper overlaps. So the visible shape is the union of the two parts. But for a puzzle, we might simplify this to just the outline.

Hmm, this is getting complex. Let me think about what's both unique AND implementable well.

Let me go with Shadow Play - it's unique, visually striking, and the math is clean (perspective projection).

Let me plan the implementation:

Let me think about the shapes. I'll use simple polygon shapes:

• Circle (approximated as polygon)
• Triangle
• Square/Rectangle
• Star
• Crescent moon
• Bird silhouette
• Rabbit ears
• etc.

For the target silhouettes, I'll create them by:

1. Setting up a specific arrangement of shapes
2. Computing the shadow
3. Saving that as the target

Or I can hand-design target silhouettes and let the player figure out the arrangement.

Let me think about the level design:

• Level 1: Single circle → match a circle shadow (learn distance = size)
• Level 2: Single triangle → match a triangle shadow (learn rotation)
• Level 3: Circle + triangle → match a specific composite
• Level 4: Star → match a star shadow
• Level 5: Multiple shapes → complex silhouette
• etc.

OK, I think this is a solid plan. Let me implement it!

Actually, wait. Let me reconsider one more time. I want to make sure this is genuinely fun and not just a tech demo. The core loop is:

1. See target silhouette
2. Place/adjust objects
3. See your shadow
4. Compare and adjust
5. Match!

This is like a reverse-engineering puzzle, which is inherently satisfying. The "aha" moment of figuring out which shapes and positions create the target shadow is the core joy.

Let me also think about what makes it more than just trial and error:

• Understanding how distance affects size (closer to light = bigger)
• Understanding how rotation affects the projected shape
• Understanding how multiple shapes combine
• Understanding overlap and layering

This has genuine educational value about optics and perspective.

OK, I'm going with Shadow Play. Let me build it!

Let me think about the technical implementation more carefully:

1. Canvas Setup: Main canvas for the game view
2. Light Source: Position at left side, with glow effect
3. Objects: Array of shape objects, each with:
   • type (circle, triangle, square, star, etc.)
   • position (x, y)
   • rotation
   • vertices (computed from type and rotation)
4. Shadow Projection: For each object, project its vertices from the light source onto the screen line
5. Screen Rendering: Draw the shadow on the right side
6. Target: Pre-defined silhouette to match
7. Scoring: IoU comparison
8. Interaction: Drag to move, scroll/keys to rotate, slider for distance

Let me think about the visual layout:

Actually, for a more immersive feel, let me make the whole canvas the stage, with the light on the left and the screen on the right, and the target shown as a ghost outline on the screen.

Let me think about the color scheme:

• Background: Deep dark blue/black (theater stage in darkness)
• Light: Warm yellow/orange glow
• Objects: Dark silhouettes (paper cutouts)
• Shadow: Dark gray/black on the screen
• Target: Dashed outline in a contrasting color (cyan/white)
• UI: Minimal, elegant

Let me start coding!

Actually, I realize I should think more carefully about the shadow projection. In a top-down view:

• Light at (lx, ly)
• Screen is a vertical line at x = screenX (right side of canvas)
• Object vertex at (vx, vy)
• Shadow point: project from light through vertex to screen
  • t = (screenX - lx) / (vx - lx)
  • shadow_y = ly + t * (vy - ly)
  • shadow_x = screenX

So the shadow is a 1D projection (a set of y-intervals) on the screen line. But we want to show it as a 2D shape on the screen.

Hmm, in a top-down view, the shadow on the screen would be a vertical strip. That's not very interesting visually.

Let me reconsider the view. Maybe a side view is better:

In a side view:

• We see the stage from the audience perspective
• The light is behind the puppets (or to the side)
• The screen is in front of us
• We see the shadow on the screen

But then the objects are between us and the screen, which makes interaction tricky.

OK, let me think about this differently. What if I use a hybrid view:

• The main view shows the screen (what the audience sees)
• The shadow is rendered on the screen
• Below or beside the screen, there's a "stage view" (top-down) where you position objects
• The target silhouette is shown on the screen as a ghost outline

This dual-view approach is common in puzzle games and would work well here.

Actually, let me simplify. What if the game is purely about the screen view, and the objects are controlled via UI controls (sliders, buttons) rather than direct manipulation on a stage?

No, that's less fun. Direct manipulation is better.

Let me try another approach: What if the "stage" is the main canvas, viewed from above, and the "screen" is the right edge? The shadow is projected onto the right edge as a 1D pattern (like a barcode). The target is also a 1D pattern. This is simpler but less visually interesting.

Hmm, that's too abstract. Let me think again...

What about a different approach entirely? Instead of light/shadow physics, what about:

Silhouette Match - You have a set of 2D shapes. You need to arrange, rotate, and scale them so that their combined silhouette matches a target outline. No light physics, just shape composition.

This is simpler to implement and still has the core puzzle mechanic. The "shadow" is just the union of the shapes' outlines.

But this loses the unique light/shadow physics that makes the game special.

Let me go back to the shadow idea but with a better view design:

Approach: Split-screen

• Top half: "Stage view" (top-down) - light on left, objects in middle, you drag objects here
• Bottom half: "Screen view" (front view) - shows the shadow projected on the screen, with target outline overlaid

The stage view is where you interact. The screen view shows the result. This is intuitive and visually clear.

For the stage view (top-down):

• Light at left
• Objects in the middle (draggable, rotatable)
• Screen line at right

For the screen view (front):

• The shadow is the projection of all objects from the light onto the screen
• In top-down, the projection gives us the y-coordinates of the shadow on the screen
• But we also need the "shape" of the shadow, not just the extent

Wait, in a real shadow puppet setup:

• The light is a point source
• The objects are 2D cutouts (flat)
• The screen is a flat surface
• The shadow is the projection of the cutout onto the screen

If the cutout is flat and parallel to the screen, the shadow is just a scaled version of the cutout. The scale depends on the distances.

If the cutout is at an angle, the shadow is a distorted (perspective) version.

In a top-down view, we can see the x-y positions. The shadow on the screen (at x = screenX) would be:

• For each point (vx, vy) on the cutout:
  • Project from light (lx, ly) to screen (screenX, ?)
  • shadow_y = ly + (vy - ly) * (screenX - lx) / (vx - lx)

But this only gives us the y-coordinate. The cutout also has a z-dimension (its shape in the direction perpendicular to the top-down view).

Hmm, I think I'm overcomplicating this. Let me simplify:

Simplified Shadow Model:

• Everything is in 2D (top-down view)
• The light is at the left
• Objects are 2D shapes (polygons)
• The screen is a vertical line on the right
• The "shadow" of each object is the projection of its polygon from the light point onto the screen line
• This gives us a set of y-intervals on the screen line
• The combined shadow is the union of all objects' shadow intervals
• The target is also a set of y-intervals

But this is just a 1D matching problem, which is too simple.

OK, let me try yet another approach. What if the objects are 2D shapes that exist in a plane, and the shadow is their 2D projection onto the screen?

Think of it this way:

• The stage is a 2D plane (the canvas)
• The light is at position (lx, ly) in this plane
• Objects are 2D shapes in this plane
• The screen is a line in this plane (right edge)
• The shadow of each object is the projection of its shape from the light onto the screen

In 2D, the projection of a polygon from a point onto a line gives us a set of intervals on that line. This is 1D.

To make it 2D, I need the objects to have extent in a third dimension. But we're in 2D canvas...

Alternative: What if the "screen" is not a line but a 2D area? Like, the shadow is cast onto a 2D surface (the right portion of the canvas), and the shadow is a 2D shape?

In this case:

• Light at (lx, ly)
• Object at (ox, oy) with shape S
• Screen is the area x > screenX
• The shadow is the projection of S from the light, clipped to the screen area

The projection of a 2D shape from a point in 2D onto a half-plane is... well, it's the set of rays from the light through the shape, intersected with the half-plane. This gives a 2D region.

Actually, this could work! The shadow would be a 2D shape (a sort of trapezoidal projection of the object). Let me think about this:

For a circle at (ox, oy) with radius r:

• The shadow is a cone from the light, clipped to the screen area
• The cone is defined by the two tangent lines from the light to the circle
• The shadow on the screen area is the region between these tangent lines, from the screen line to the right edge

For a polygon:

• The shadow is the region bounded by the projections of the polygon's edges

This is essentially computing the "shadow volume" in 2D. It's doable!

The shadow of a convex polygon from a point light:

1. Find the two tangent vertices (the ones that are "visible" from the light and form the silhouette)
2. The shadow is the polygon formed by: the two tangent vertices, their projections on the screen, and the screen edge between the projections

For non-convex shapes, it's more complex, but I can use convex shapes for simplicity.

Actually, let me think about this more simply. The shadow of an object on the screen area is:

For each vertex of the object, project it from the light to the far edge of the canvas. The shadow is the convex hull of: the object's vertices and their projections.

No wait, that's not right either. The shadow is the region that is "behind" the object from the light's perspective. It's the set of points that are on the screen side of the object and are blocked by the object from the light.

For a convex polygon, the shadow is:

1. Find the two tangent lines from the light to the polygon
2. The shadow is the region bounded by:
   • The two tangent lines (from the tangent points to the far edge)
   • The far edge of the canvas
   • The part of the polygon between the two tangent points (facing away from the light)

This is the "shadow volume" approach. Let me implement this:

For a convex polygon with vertices V0, V1, ..., Vn:

1. Find the two tangent vertices (the ones with the smallest and largest angle from the light)
2. The shadow polygon is:
   • Start at tangent vertex A
   • Go along the polygon away from the light to tangent vertex B
   • Project B from the light to the far edge → point B'
   • Go along the far edge to A's projection A'
   • Close the polygon

This gives us the shadow region. We can render this as a dark shape on the canvas.

For the target, we can pre-compute the shadow of a specific arrangement and use that as the target.

For scoring, we compare the player's shadow with the target using pixel-based IoU.

OK, I think this is implementable! Let me go with this approach.

But wait, I need to think about whether this is actually fun. The player:

1. Sees a target shadow shape on the right side of the canvas
2. Has objects they can drag around the stage (left/center)
3. As they move objects, the shadow changes in real-time
4. They need to match the target shadow

The fun comes from:

• Figuring out which shapes create which shadows
• Understanding how distance affects shadow size
• Understanding how rotation affects the shadow
• Combining multiple shapes
• The satisfaction of matching the target

I think this is fun! It's like a reverse puzzle - you see the result and need to figure out the cause.

Let me also think about the visual style:

• Dark theater stage
• Warm light glow on the left
• Objects as dark cutout shapes
• Shadow as dark gray region on the right
• Target as a glowing outline
• Elegant, minimal UI

OK, let me start implementing. I'll create the game at /space/games/shadow-play/index.html.

Let me think about the full implementation plan:

1. HTML structure: canvas + UI overlay
2. CSS: dark theater theme, elegant UI
3. JavaScript: a. Game state (current level, objects, score) b. Shape definitions (circle, triangle, square, star, etc.) c. Shadow computation (tangent-based projection) d. Canvas rendering (light, objects, shadow, target) e. Interaction (drag, rotate, add/remove shapes) f. Level system (target shadows, increasing complexity) g. Scoring (IoU comparison) h. Audio (ambient theater sounds, success chimes)

Let me think about the shapes I'll use:

• Circle (approximated as 32-gon)
• Triangle
• Square
• Star (5-pointed)
• Diamond
• Hexagon
• Crescent (circle minus offset circle)

For levels, I'll create target shadows by:

1. Defining a specific arrangement of shapes
2. Computing the shadow
3. Using that as the target

Or I can hand-craft target silhouettes as polygons and let the player figure out the arrangement.

I think hand-crafting targets is better because it gives more control over the puzzle design. The player has a set of shapes available and needs to figure out which ones to use and how to position them.

Let me design 10 levels:

Level 1: "First Light" - Match a simple circle shadow. One circle available. Learn: distance = size. Level 2: "Triangle" - Match a triangle shadow. One triangle available. Learn: rotation matters. Level 3: "Growing" - Match a large circle shadow. One circle available. Learn: closer to light = bigger. Level 4: "Double Act" - Match a shadow with two separate parts. Two circles available. Level 5: "Star Light" - Match a star shadow. One star available. Level 6: "The Bird" - Match a bird-like silhouette. Triangle + circle available. Level 7: "Castle" - Match a castle silhouette. Multiple rectangles and triangles. Level 8: "The Rabbit" - Match a rabbit silhouette. Multiple shapes. Level 9: "Landscape" - Match a landscape silhouette. Multiple shapes. Level 10: "Grand Finale" - Complex silhouette with many shapes.

Actually, for the shadow computation, I need to be more careful. Let me think about this again.

In my model:

• Light at (lx, ly) - a point on the left side
• Screen area: the right portion of the canvas (x > screenX)
• Objects: 2D convex polygons in the stage area (between light and screen)

The shadow of an object is the region on the screen side that is blocked by the object from the light. For a convex polygon:

1. Compute the angle from the light to each vertex
2. Find the two "extreme" vertices (min and max angle) - these are the tangent vertices
3. The shadow is the polygon formed by:
   • The tangent vertices and the vertices between them (on the far side from the light)
   • The projections of the tangent vertices onto the far edge of the canvas

Wait, I need to be more precise. Let me think about this with a specific example:

Light at (100, 300) Object: square at (400, 300) with vertices at (380,280), (420,280), (420,320), (380,320) Screen at x = 600 Canvas width = 800

The shadow of this square:

• From the light, the tangent lines touch the square at (380,280) and (380,320) (the left edge, closest to the light)
• Wait, no. The tangent lines from an external point to a convex polygon touch the polygon at the vertices that are "extreme" in terms of angle.

Let me compute the angles:

• (380,280): angle = atan2(280-300, 380-100) = atan2(-20, 280) ≈ -4°
• (420,280): angle = atan2(280-300, 420-100) = atan2(-20, 320) ≈ -3.6°
• (420,320): angle = atan2(320-300, 420-100) = atan2(20, 320) ≈ 3.6°
• (380,320): angle = atan2(320-300, 380-100) = atan2(20, 280) ≈ 4°

So the extreme vertices are (380,280) at -4° and (380,320) at 4°. These are the left edge vertices (closest to the light).

The shadow polygon:

• Start at (380,280) - upper tangent vertex
• The far side of the polygon from the light goes: (380,280) → (420,280) → (420,320) → (380,320)
• So the far side is: (420,280), (420,320) (the right edge)
• Wait, I need to identify which vertices are on the "far side" (the silhouette edge facing away from the light)

The tangent vertices are (380,280) and (380,320). The polygon vertices in order are: (380,280), (420,280), (420,320), (380,320).

Going from (380,280) to (380,320) the "long way" (away from the light): (380,280) → (420,280) → (420,320) → (380,320).

So the shadow polygon is:

1. (380,280) - upper tangent
2. (420,280) - far side
3. (420,320) - far side
4. (380,320) - lower tangent
5. Project (380,320) from light to far edge:
   • t = (800 - 100) / (380 - 100) = 700/280 = 2.5
   • shadow_y = 300 + 2.5 * (320 - 300) = 300 + 50 = 350
   • → (800, 350)
6. Go along far edge to upper projection:
   • Project (380,280) from light to far edge:
   • shadow_y = 300 + 2.5 * (280 - 300) = 300 - 50 = 250
   • → (800, 250)
7. Close back to (380,280)

So the shadow polygon is: (380,280), (420,280), (420,320), (380,320), (800,350), (800,250)

This is a hexagonal shape that starts at the object, widens as it goes to the right. This is the shadow!

For rendering, I'll fill this polygon with a dark color. The shadow gets darker/more opaque closer to the object and lighter farther away (but for simplicity, I can use a uniform dark color or a gradient).

For multiple objects, I need to compute the union of all shadows. This can be done by:

1. Rendering each shadow to an offscreen canvas
2. Compositing them together (union = draw all with same color)

For the target, I'll define it as a polygon or as a set of shapes that produce a specific shadow.

For scoring, I'll:

1. Render the player's shadow to an offscreen canvas (white on black)
2. Render the target to another offscreen canvas (white on black)
3. Compare pixels: IoU = intersection / union

OK, I think I have a solid plan. Let me implement this!

Actually, let me reconsider the complexity. Computing tangent vertices for convex polygons is straightforward, but I need to handle:

• Objects between the light and the screen
• Objects at various angles
• Multiple objects with overlapping shadows
• Non-convex shapes (crescent, star)

For non-convex shapes, I can decompose them into convex parts or use a different approach:

• For each shape, compute the shadow by casting rays from the light through each vertex and finding the silhouette edges.

Actually, for simplicity, let me use a different approach for shadow computation:

Ray-based approach:

1. For each object, cast rays from the light through each vertex
2. The shadow is the region between the "leftmost" and "rightmost" rays (in terms of angle), bounded by the object and the canvas edge

For convex shapes, this is equivalent to the tangent approach. For non-convex shapes, it's an approximation but should look reasonable.

Actually, the simplest approach is:

Silhouette approach:

1. For each object, find the silhouette edges (edges where one face is toward the light and the other is away)
2. The shadow is the extrusion of these edges from the object to the canvas edge

For a convex polygon:

• An edge is a silhouette edge if the light is on the "outside" of that edge
• The shadow is formed by the two tangent vertices and the far-side edges

Let me just implement the tangent approach for convex polygons and decompose non-convex shapes into convex parts.

Actually, for the initial implementation, let me use only convex shapes (circle, triangle, square, hexagon, diamond). I can add star and crescent later if needed.

For a circle (approximated as a 32-gon), the tangent points are the two points on the circle where the line from the light is tangent to the circle. These can be computed analytically:

Given light at L, circle center at C, radius r:

• d = distance(L, C)
• If d <= r, the light is inside the circle (no shadow, or the circle blocks all light)
• Otherwise:
  • a = asin(r / d)
  • The angle to the center: θ = atan2(C.y - L.y, C.x - L.x)
  • Upper tangent angle: θ + a
  • Lower tangent angle: θ - a
  • Upper tangent point: C + r * (cos(θ + a + π/2), sin(θ + a + π/2))...

Hmm, this is getting complicated. Let me just use the polygon approximation for circles and use the general convex polygon tangent approach.

For a convex polygon with vertices V[0], V[1], ..., V[n-1] (in order):

1. Compute the angle from the light to each vertex
2. Find the vertex with the minimum angle (upper tangent) and the vertex with the maximum angle (lower tangent)
3. The shadow polygon is:
   • From the upper tangent vertex, follow the polygon edges away from the light to the lower tangent vertex
   • From the lower tangent vertex, project to the canvas edge
   • Along the canvas edge to the upper tangent vertex's projection
   • Back to the upper tangent vertex

Wait, I need to be careful about which direction is "away from the light". The vertices between the two tangent vertices on the far side (away from the light) form the back silhouette.

Let me think about this more carefully:

For a convex polygon with vertices in counterclockwise order:

• The upper tangent vertex is the one with the smallest angle (most clockwise from the light's perspective)
• The lower tangent vertex is the one with the largest angle (most counterclockwise)
• The "far side" is the chain of vertices from the upper tangent to the lower tangent going counterclockwise (the side away from the light)

Actually, I think the simplest approach is:

1. For each vertex, compute the angle from the light
2. Sort vertices by angle
3. The tangent vertices are the ones with min and max angle
4. The shadow is the polygon: [tangent_min, ...far_side_vertices..., tangent_max, projection_of_tangent_max, projection_of_tangent_min]

Where the far_side_vertices are the vertices between tangent_min and tangent_max going the "long way" around the polygon (away from the light).

Hmm, this is getting complex. Let me use a simpler approach:

Simple shadow approach:

1. For each vertex of the object, project it from the light to the far edge of the canvas
2. The shadow polygon is the convex hull of: [all object vertices, all projected vertices]

Wait, that's not right either. The shadow is not the convex hull.

OK, let me think about this differently. The shadow of a convex object from a point light is a "shadow volume" - a cone-like shape from the object to the far edge.

For a convex polygon, the shadow volume is:

1. Find the two tangent vertices (extreme angles from light)
2. The shadow polygon is:
   • Start at tangent vertex A (min angle)
   • Follow the polygon boundary away from the light to tangent vertex B (max angle)
   • Project B to the far edge → B'
   • Follow the far edge to A's projection → A'
   • Close back to A

The key is identifying which boundary path from A to B is "away from the light". For a convex polygon, this is the path that doesn't include any vertices that are closer to the light than A and B.

Actually, for a convex polygon, the tangent vertices divide the boundary into two chains:

• The "near" chain (facing the light) - this is the shorter path between the tangent vertices
• The "far" chain (away from the light) - this is the longer path

The shadow uses the far chain.

For a convex polygon with vertices in CCW order:

• If the light is to the left of the polygon, the near chain is on the left side and the far chain is on the right side
• The tangent vertices are the top-left and bottom-left vertices (approximately)

Let me just implement this with a simple algorithm:

This is getting complicated. Let me simplify by using a different approach entirely.

Approach: Render-based shadow Instead of computing the shadow polygon analytically, I can:

1. Render each object as a solid shape on an offscreen canvas
2. For the shadow, render the object from the light's perspective as a "projection"
3. Use canvas compositing to create the shadow

Actually, here's a simpler idea:

Approach: Triangle fan projection For each edge of the polygon, create a triangle (or quad) from the edge to its projection on the far edge. The shadow is the union of all these triangles.

For a convex polygon, this is equivalent to the tangent approach but simpler to implement:

Wait, is this correct? Let me check with the square example:

Vertices: (380,280), (420,280), (420,320), (380,320) Light: (100, 300) farX: 800

Projections:

• (380,280): t = 700/280 = 2.5, y = 300 + 2.5*(-20) = 250 → (800, 250)
• (420,280): t = 700/320 = 2.1875, y = 300 + 2.1875*(-20) = 256.25 → (800, 256.25)
• (420,320): t = 700/320 = 2.1875, y = 300 + 2.1875*(20) = 343.75 → (800, 343.75)
• (380,320): t = 700/280 = 2.5, y = 300 + 2.5*(20) = 350 → (800, 350)

Shadow polygon: (380,280), (420,280), (420,320), (380,320), (800,350), (800,343.75), (800,256.25), (800,250)

Hmm, the projections on the far edge are: (800,250), (800,256.25), (800,343.75), (800,350). These are all on the line x=800, so the last four points are collinear. The effective shadow polygon is: (380,280), (420,280), (420,320), (380,320), (800,350), (800,250).

This is the same as what I computed before with the tangent approach! The intermediate projection points (256.25 and 343.75) are between 250 and 350, so they don't add anything.

But wait, is this always correct? For a convex polygon, the projection of all vertices onto the far edge will be within the range of the tangent projections. So the simple approach of [all vertices, all projections reversed] gives the correct shadow polygon (with some redundant collinear points).

Actually, I'm not sure this is always correct. Consider a triangle:

Vertices: (400,200), (500,300), (400,400) Light: (100, 300) farX: 800

Projections:

• (400,200): t = 700/300 = 2.333, y = 300 + 2.333*(-100) = 66.67 → (800, 66.67)
• (500,300): t = 700/400 = 1.75, y = 300 + 1.75*0 = 300 → (800, 300)
• (400,400): t = 700/300 = 2.333, y = 300 + 2.333*(100) = 533.33 → (800, 533.33)

Shadow polygon: (400,200), (500,300), (400,400), (800,533.33), (800,300), (800,66.67)

Is this correct? The shadow should be the cone from the light through the triangle, projected to the far edge. The tangent vertices from the light (100,300) to the triangle are (400,200) and (400,400) (the left edge). The far vertex is (500,300).

The shadow should be: (400,200) → (500,300) → (400,400) → (800,533.33) → (800,66.67) → back to (400,200).

With the simple approach, I get: (400,200), (500,300), (400,400), (800,533.33), (800,300), (800,66.67).

The extra point (800,300) is between (800,66.67) and (800,533.33), so it's redundant (collinear). So the simple approach gives the correct result!

But what about a case where the projection of a vertex is outside the tangent range? For a convex polygon, this shouldn't happen because the tangent vertices define the extreme angles, and all other vertices are within that angular range. So their projections will be within the tangent projections.

Wait, actually, that's not necessarily true. The projection depends on both the angle and the distance. A vertex that's at a middle angle but closer to the light will have a projection that's farther from the center... no, let me think again.

The projection y-coordinate is: y' = ly + t * (vy - ly) where t = (farX - lx) / (vx - lx).

For a vertex at angle θ from the light: vy - ly = d * sin(θ), vx - lx = d * cos(θ), where d is the distance from the light.

So y' = ly + (farX - lx) / (d * cos(θ)) * d * sin(θ) = ly + (farX - lx) * tan(θ).

The projection depends only on the angle, not the distance! So for a convex polygon, all vertices are within the angular range of the tangent vertices, and their projections are within the tangent projections. The simple approach is correct!

Great, so the simple approach works:

This gives a polygon that represents the shadow of a convex object. For non-convex objects, I'd need to decompose them, but I'll stick with convex shapes for now.

For multiple objects, I'll render each shadow to an offscreen canvas and composite them (using globalCompositeOperation = 'source-over' with the same fill color, which gives the union).

Now, for the target silhouettes, I have two options:

1. Define a specific arrangement of shapes, compute the shadow, and use that as the target
2. Hand-draw target silhouettes as polygons

Option 1 is easier to implement and ensures the puzzle is solvable. Option 2 gives more creative freedom but requires manual drawing.

I'll go with Option 1: define the solution arrangement, compute the shadow, and present it as the target. The player needs to figure out the arrangement.

But wait, there's a subtlety: the player might find a different arrangement that produces the same shadow. That's fine - multiple solutions are OK!

Let me also think about the interaction model:

• The player has a palette of shapes at the bottom
• They click a shape to add it to the stage
• They drag shapes to position them
• They rotate shapes with a rotation handle or keyboard
• They can delete shapes
• The shadow updates in real-time
• The target is shown as an outline on the screen
• A "Check" button compares the shadow with the target and gives a score

For the visual design:

• Dark background (#0a0a0f or similar)
• Light source: warm yellow glow on the left
• Stage area: slightly lighter than background
• Screen area: lighter panel on the right
• Objects: dark silhouettes (almost black)
• Shadow: dark gray on the screen
• Target: glowing cyan/white outline
• UI: minimal, elegant, warm accents

Let me also think about audio:

• Ambient: soft theater ambiance (low hum, occasional creaks)
• Interaction: soft "paper" sounds when moving shapes
• Success: warm chime when matching the target
• Background: subtle, atmospheric

I'll use Web Audio API for procedural sounds.

OK, I think I have a comprehensive plan. Let me start coding!

Let me also think about the level structure more carefully:

Level 1: "First Light"

• Target: A medium circle shadow
• Available: 1 circle
• Solution: Place circle at medium distance from light
• Teaches: Basic placement

Level 2: "Size Matters"

• Target: A large circle shadow
• Available: 1 circle
• Solution: Place circle close to the light
• Teaches: Closer = bigger

Level 3: "Small World"

• Target: A small circle shadow
• Available: 1 circle
• Solution: Place circle far from light (close to screen)
• Teaches: Farther = smaller

Level 4: "Triangle"

• Target: A triangle shadow pointing right
• Available: 1 triangle
• Solution: Place triangle with point facing the screen
• Teaches: Rotation affects shadow shape

Level 5: "Inverted"

• Target: A triangle shadow pointing left (inverted)
• Available: 1 triangle
• Solution: Place triangle with point facing the light
• Teaches: The shadow inverts the shape

Level 6: "Double Vision"

• Target: Two separate circle shadows
• Available: 2 circles
• Solution: Place two circles at different heights
• Teaches: Multiple objects create multiple shadows

Level 7: "The Star"

• Target: A star-shaped shadow
• Available: 1 star
• Solution: Place star at the right distance and rotation
• Teaches: Complex shapes create complex shadows

Level 8: "The Bird"

• Target: A bird-like silhouette (circle body + triangle beak)
• Available: 1 circle, 1 triangle
• Solution: Combine shapes to create a bird shadow
• Teaches: Combining shapes

Level 9: "The Castle"

• Target: A castle silhouette (rectangles + triangles)
• Available: 2 rectangles, 2 triangles
• Solution: Build a castle shadow
• Teaches: Complex composition

Level 10: "Grand Finale"

• Target: A complex silhouette
• Available: Multiple shapes
• Solution: Complex arrangement
• Teaches: Mastery

This is a good progression! Let me implement it.

Now, for the target computation, I need to:

1. Define the solution arrangement (shapes with positions and rotations)
2. Compute the shadow of this arrangement
3. Render it to an offscreen canvas
4. Use that as the target

For scoring:

1. Render the player's shadow to an offscreen canvas
2. Compare with the target canvas pixel by pixel
3. Compute IoU (Intersection over Union)
4. Score = IoU * 100

Let me think about the canvas dimensions:

• Main canvas: 1000 x 600 (or responsive)
• Light at x = 80
• Screen at x = 700
• Stage area: x = 80 to 700
• Screen area: x = 700 to 1000

Actually, let me make the screen area wider for better shadow visibility:

• Light at x = 60
• Stage area: x = 60 to 500
• Screen at x = 500
• Screen area: x = 500 to 980

Hmm, let me think about this differently. The shadow extends from the object to the far edge of the canvas. So the "screen" is really the far edge. The shadow is visible in the area between the objects and the far edge.

Let me redesign:

• Light at x = 50 (left edge)
• Stage area: x = 50 to 500 (where objects are placed)
• Shadow area: x = 500 to 950 (where shadows are cast)
• The "screen" is at x = 950 (right edge)

The target silhouette is shown in the shadow area (x = 500 to 950).

Actually, I think the cleanest design is:

• The entire canvas is the stage
• Light on the far left
• Objects placed in the left-center
• Shadows cast to the right
• Target outline shown in the right portion

Let me use a canvas of 960 x 600:

• Light at (50, 300)
• Objects placed in x: 100-450
• Shadow visible in x: 450-910
• Target outline in x: 450-910

For the target, I'll render it as a filled silhouette in a semi-transparent color, with a glowing outline.

OK, let me start coding now. I'll write the complete game in a single HTML file.

Let me think about the code structure:

Let me now write the full implementation. I'll be thorough and make it polished.

Actually, let me reconsider the shapes. For the shadow to be interesting, I need shapes that produce different shadows at different rotations:

• Circle: shadow is always the same shape (a cone), rotation doesn't matter. Good for teaching distance.
• Triangle: shadow changes with rotation. Good for teaching rotation.
• Square: shadow changes with rotation (from a rectangle to a more trapezoidal shape).
• Star: complex shadow that changes with rotation.
• Hexagon: moderate complexity.

For the star, it's non-convex, so my simple shadow approach won't work perfectly. Let me decompose the star into triangles or use a different approach.

Actually, for a non-convex shape, the simple approach of [vertices, projections reversed] won't give a correct shadow because the polygon will be self-intersecting. I need to handle non-convex shapes differently.

For non-convex shapes, I can:

1. Decompose into convex parts and compute shadows for each part
2. Use a different shadow algorithm (like computing the silhouette edges)

For a star (5-pointed), I can decompose it into 5 triangles from the center. Each triangle is convex, and I compute the shadow for each. The union of these shadows is the star's shadow.

Actually, for the star, the shadow will be the same as the convex hull's shadow because the "indentations" of the star are on the near side (facing the light) or the far side (away from the light), and the shadow is determined by the silhouette edges.

Hmm, this is getting complex. Let me just use convex shapes for now: circle, triangle, square, hexagon, diamond. I can add the star later if I figure out the non-convex shadow.

Actually, wait. For the star, I can use the convex hull approach: the shadow of a non-convex shape is the same as the shadow of its convex hull (from a point light, the shadow is determined by the silhouette, which for a non-convex shape is the convex hull's silhouette).

Is this true? No, it's not. The shadow of a non-convex shape can have "holes" or indentations that the convex hull's shadow wouldn't have. But from a point light, the shadow is the projection of the shape's silhouette, which is the convex hull of the shape as seen from the light. In 2D, the silhouette from a point is the two tangent lines, and the shadow is the cone between them. So yes, the shadow of any shape from a point light is the same as the shadow of its convex hull.

Wait, that's only true if the shape is "solid" (filled). If the shape has holes, the shadow would have holes too. But for our purposes, all shapes are solid, so the shadow is the same as the convex hull's shadow.

So for a star, the shadow is the same as the shadow of its convex hull (which is a pentagon). The star's points don't create a star-shaped shadow; they create a pentagon-shaped shadow.

Hmm, that's not very interesting. The star would look the same as a pentagon in the shadow. Let me reconsider.

Actually, wait. The shadow of a 2D shape from a point light in 2D is NOT the same as the convex hull's shadow. The shadow is the projection of the shape's outline, and for a non-convex shape, the outline has indentations that affect the shadow.

Let me think again. In 2D, the shadow of a shape from a point light is the set of points on the far side that are "blocked" by the shape. For a convex shape, this is a cone. For a non-convex shape, it's more complex.

For a star, the shadow would be the union of the shadows of its convex parts. If I decompose the star into 5 triangles (from center to each pair of adjacent outer vertices), the shadow is the union of the 5 triangle shadows.

But actually, the union of the triangle shadows is the same as the convex hull's shadow because the triangles fill the convex hull. So the star's shadow is the same as the pentagon's shadow.

Hmm, but that's only true if the star is "filled" (solid). If the star is just the outline (wireframe), the shadow would be different. But for our game, shapes are solid, so the shadow is the convex hull's shadow.

OK, so for solid shapes, the shadow from a point light in 2D is always the convex hull's shadow. This means:

• Circle → cone shadow (always the same regardless of rotation)
• Triangle → cone shadow (changes with rotation because the convex hull is the triangle itself)
• Square → cone shadow (changes with rotation)
• Star → same as pentagon shadow (changes with rotation, but the star points don't show)

This means the star is not interesting because it looks like a pentagon. Let me drop the star and use:

• Circle (distance teaching)
• Triangle (rotation teaching)
• Square (rotation teaching)
• Hexagon (rotation teaching, more complex)
• Diamond (rotation teaching, different shape)

Actually, wait. I was wrong. The shadow of a solid 2D shape from a point light is NOT the convex hull's shadow. Let me reconsider.

In 2D, the shadow of a shape from a point light is the set of points P such that the line from the light to P intersects the shape. For a convex shape, this is a cone (the tangent lines define the boundary). For a non-convex shape, the shadow can have a more complex boundary.

For a star, the line from the light to a point on the far edge might pass through a "valley" of the star, creating a non-convex shadow boundary.

Wait, no. If the shape is solid (filled), then any line from the light that intersects the shape at all will be blocked. The shadow is the set of directions from the light that are blocked by the shape. For a solid shape, this is the set of directions that intersect the shape, which is the same as the set of directions that intersect the convex hull (because if a direction intersects the shape, it intersects the convex hull, and vice versa).

Hmm, is that true? If a ray from the light passes through a "valley" of the star (between two points), does it intersect the star? If the star is solid (filled), then yes, the ray passes through the interior of the star. So the ray is blocked.

Actually, for a solid star, the ray from the light through a valley of the star does pass through the star's interior (the star is filled, including the valley regions between the points). Wait, no. A 5-pointed star is typically drawn as a non-convex polygon. The "valleys" are outside the polygon. So a ray through a valley does NOT intersect the star.

Let me reconsider. A 5-pointed star polygon has 10 vertices: 5 outer points and 5 inner points. The polygon goes: outer, inner, outer, inner, ... The interior of this polygon does NOT include the "valley" regions between the outer points. So a ray through a valley does NOT intersect the star.

Therefore, the shadow of a star is NOT the same as the convex hull's shadow. The star's shadow will have a star-like shape (with indentations corresponding to the valleys).

So my earlier conclusion was wrong. The shadow of a non-convex solid shape is different from its convex hull's shadow. Good, this means the star is interesting!

But then my simple shadow algorithm (vertices + projections reversed) won't work for non-convex shapes because the resulting polygon will be self-intersecting.

For non-convex shapes, I need a different approach. Let me think...

Approach for non-convex shapes:

1. Cast rays from the light through each vertex of the shape
2. Sort the rays by angle
3. For each pair of adjacent rays, determine if the region between them is in shadow or not
4. The shadow boundary is the set of rays where the "in shadow" status changes

This is essentially computing the "visibility" from the light's perspective. For each angular slice between two adjacent vertex rays, the slice is in shadow if the ray through the midpoint intersects the shape.

This is more complex but doable. However, for simplicity, let me use a different approach:

Approach: Render-based shadow for non-convex shapes

1. Render the shape to an offscreen canvas (solid fill)
2. For the shadow, use a "projection" rendering: for each column of pixels between the shape and the far edge, check if the corresponding ray from the light intersects the shape
3. This is essentially a 1D projection for each y-coordinate

Actually, this is getting too complex. Let me use a simpler approach:

Approach: Decompose non-convex shapes into convex parts For a star, decompose it into 5 triangles (center to each pair of adjacent vertices). Compute the shadow for each triangle (convex) and take the union.

The union of the 5 triangle shadows will correctly represent the star's shadow, including the indentations.

Let me implement this:

For rendering, I'll render each shadow polygon to the canvas. For unions, I'll render each part with the same fill color.

OK, this is workable. Let me implement the full game now.

Actually, let me simplify even further. For the initial implementation, I'll use only convex shapes (circle, triangle, square, hexagon, diamond). This keeps the shadow computation simple. I can add the star later if needed.

For the levels, I'll use combinations of convex shapes to create interesting target shadows.

Let me finalize the level design:

Level 1: "First Light" - 1 circle, match a medium circle shadow Level 2: "Big and Small" - 1 circle, match a large circle shadow (close to light) Level 3: "Turning Point" - 1 triangle, match a triangle shadow (specific rotation) Level 4: "Square Dance" - 1 square, match a square shadow (specific rotation) Level 5: "Twin Suns" - 2 circles, match two separate circle shadows Level 6: "The Bird" - 1 circle + 1 triangle, match a bird-like shadow Level 7: "Hexagonal" - 1 hexagon, match a hexagon shadow Level 8: "The Mountain" - 2 triangles, match a mountain-like shadow Level 9: "The Castle" - 2 squares + 2 triangles, match a castle shadow Level 10: "Grand Finale" - multiple shapes, match a complex shadow

For each level, I'll define the solution arrangement and compute the target shadow from it.

Let me now write the code!

Actually, I realize I should think about one more thing: the target shadow rendering. The target is the shadow of the solution arrangement. I need to:

1. Place the solution shapes at their positions
2. Compute their shadows
3. Render the shadows to an offscreen canvas
4. Display this as the target (with a glowing outline)

For the player's shadow, I do the same thing with the player's current arrangement.

For scoring, I compare the two offscreen canvases pixel by pixel.

Let me also think about the visual presentation of the target. I'll show it as:

• A semi-transparent filled silhouette in a cool color (cyan/blue)
• A glowing outline around the silhouette
• The player's shadow in a warm color (dark gray/black) on top

When the player's shadow matches the target, the colors blend and the outline glows green.

OK, let me start writing the code now. I'll create a comprehensive, polished game.

Let me think about the overall HTML structure:

Actually, for a more immersive experience, let me put everything on the canvas and use HTML/CSS only for the UI overlay. The canvas will render the stage, light, objects, shadows, and target. The UI overlay will have the shape palette, controls, and level info.

Let me think about the layout more carefully:

The canvas takes up most of the space. The UI is overlaid on top.

Let me think about responsive design

The error is at line 125 of the JavaScript, which corresponds to a comment block that contains what looks like YAML or pseudo-code. Let me find and fix this. The issue is in the comment block for the LEVELS definition where I have:

The - name: display name line is being parsed as JavaScript because it's not properly commented. Let me find and fix this.

I see some issues with the level solutions:

1. Twin Shadows: The shadows extend way off-screen (y=-703 to y=-290 and y=890 to y=1303). The circles are at y=0.32 and y=0.68 of the height (192 and 408), but the shadow projection magnifies the offset. The shadows are completely off-screen! I need to move the circles closer to the center or closer to the screen.

2. Grand Finale: The triangles at y=0.35 and y=0.65 (210 and 390) also have shadows that go off-screen (y=-418 to y=-106 and y=706 to y=1018). Same issue.

The problem is that the perspective projection amplifies the y-offset. When an object is at y=192 (offset of -108 from light at y=300), and the object is at x=179 (distance of 119 from light at x=60), the projection to farX=940 gives:

• t = (940 - 60) / (179 - 60) = 880 / 119 ≈ 7.39
• shadow_y = 300 + 7.39 * (192 - 300) = 300 + 7.39 * (-108) = 300 - 798 = -498

So the shadow is at y=-498, which is way off-screen. The magnification factor is about 7.4x, which means even a small y-offset gets amplified enormously.

To fix this, I need to either:

1. Move the objects closer to the screen (larger x values) to reduce the magnification
2. Move the objects closer to the center (y closer to 0.5) to reduce the y-offset
3. Increase the distance between the light and the screen

Let me recalculate. For the shadow to stay on-screen (0 to 600), with the light at y=300:

• The maximum y-offset at the far edge is 300 (to reach y=0 or y=600)
• The magnification factor is t = (farX - lightX) / (objX - lightX) = (940 - 60) / (objX - 60) = 880 / (objX - 60)
• For the shadow to stay on-screen: |offset| * t <= 300
• So |offset| <= 300 / t = 300 * (objX - 60) / 880

For an object at x=179 (distance 119 from light):

• t = 880 / 119 ≈ 7.39
• max offset = 300 / 7.39 ≈ 40.6
• So the object must be within y=300±40, i.e., y=260 to y=340

For an object at x=252 (distance 192 from light):

• t = 880 / 192 ≈ 4.58
• max offset = 300 / 4.58 ≈ 65.5
• So the object must be within y=300±65, i.e., y=235 to y=365

For the Twin Shadows level, I need the two circles to be far enough apart to create separate shadows, but close enough to the center to stay on-screen. Let me move them closer to the screen:

If I place them at x=0.35 (x = 100 + 0.35 * 360 = 226, distance 166 from light):

• t = 880 / 166 ≈ 5.3
• max offset = 300 / 5.3 ≈ 56.6
• So y can be 300±56, i.e., 244 to 356
• For two separate shadows, I need them at least 2*size apart in shadow space
• Shadow size at this distance: 28 * 5.3 ≈ 148 pixels each
• So the shadows would be about 148 pixels wide each
• For them to be separate, the centers need to be at least 148 pixels apart in shadow space
• In object space, that's 148 / 5.3 ≈ 28 pixels apart
• So y1 = 300 - 28 = 272, y2 = 300 + 28 = 328
• Normalized: y1 = 272/600 = 0.453, y2 = 328/600 = 0.547

Hmm, that's very close together. The shadows would barely be separate. Let me think about this differently.

Actually, the issue is that the magnification is too high because the objects are close to the light and the screen is far away. Let me adjust the layout:

• Move the light closer to the center, or
• Move the screen closer, or
• Make the stage area wider

Actually, the real issue is that the farX is too far. Let me reduce the canvas projection distance. Instead of projecting to the far edge of the canvas, I should project to the screen line (screenX), not farX.

Wait, no. The shadow is cast FROM the object TO the screen. The screen is at screenX. The shadow appears ON the screen. So the projection should be to screenX, not farX!

Let me re-read my code... In computeShadowPolygon, I project to farX. But the shadow should be on the screen at screenX. The area between screenX and farX is the "screen surface" where the shadow is visible.

Actually, I think the issue is conceptual. In a real shadow puppet theater:

• The light is on one side
• The puppets are between the light and the screen
• The screen is a flat surface
• The shadow is cast ON the screen

In my 2D top-down view:

• The light is at the left
• The objects are in the middle
• The "screen" is a vertical line at screenX
• The shadow is the projection of the objects from the light onto the screen line

But a projection onto a line gives a 1D result (a set of y-intervals). To make it 2D, I've been projecting to the far edge (farX) and filling the area between the object and the far edge. This creates a 2D shadow region.

The problem is that the magnification factor depends on the distance from the light to the far edge, which is very large (880 pixels). This causes extreme magnification.

To fix this, I should either:

1. Reduce the distance to the projection plane (use screenX instead of farX)
2. Accept the high magnification and adjust the level solutions accordingly

If I use screenX as the projection plane:

• screenX = 460
• For an object at x=200 (distance 140 from light):
  • t = (460 - 60) / (200 - 60) = 400 / 140 ≈ 2.86
  • max offset = 300 / 2.86 ≈ 105
  • So y can be 300±105, i.e., 195 to 405

This is much more reasonable! The shadows would be about 2.86x magnified, which is manageable.

But then the shadow would only extend from the object to screenX, not to farX. The area between screenX and farX would be the "screen surface" where the shadow is displayed.

Actually, I think the better approach is:

1. Project the shadow to screenX (the screen line)
2. Display the shadow in the area between the object and screenX
3. The target silhouette is shown in the screen area (between screenX and farX)

But this means the shadow and the target are in different areas, which is confusing.

Let me reconsider the layout. Maybe I should:

1. Have the light on the left
2. The stage (objects) in the center-left
3. The screen on the right, showing both the player's shadow and the target
4. The shadow is projected from the light through the objects onto the screen

The key insight is that the "screen" is where the shadow appears. The shadow is a 2D shape on the screen. In my top-down view, the screen is a vertical line, and the shadow is a 1D projection. But I want to show it as a 2D shape.

Alternative approach: Instead of a top-down view, use a "side view" where:

• We see the screen from the front
• The shadow is a 2D shape on the screen
• The objects are controlled via a separate mini-map or controls

This is more complex but would give a proper 2D shadow.

Actually, let me reconsider. The current approach works, but the magnification is too high. Let me just adjust the level solutions to keep the shadows on-screen.

The key formula: for an object at (x, y) with the light at (lx, ly) and projection to fx:

• shadow_y = ly + (fx - lx) / (x - lx) * (y - ly)
• magnification = (fx - lx) / (x - lx)

For the shadow to be on-screen (0 to H):

• |shadow_y - ly| < H/2
• |y - ly| * magnification < H/2
• |y - ly| < H/2 / magnification = H/2 * (x - lx) / (fx - lx)

With H=600, lx=60, fx=940:

• |y - 300| < 300 * (x - 60) / 880

For x=200: |y - 300| < 300 * 140 / 880 = 47.7 → y in [252, 348] For x=250: |y - 300| < 300 * 190 / 880 = 64.8 → y in [235, 365] For x=300: |y - 300| < 300 * 240 / 880 = 81.8 → y in [218, 382] For x=350: |y - 300| < 300 * 290 / 880 = 98.9 → y in [201, 399] For x=400: |y - 300| < 300 * 340 / 880 = 115.9 → y in [184, 416]

So for the Twin Shadows level, if I place the circles at x=0.35 (x=226):

• |y - 300| < 300 * 166 / 880 = 56.6 → y in [243, 357]
• For two separate shadows, I need them at different y values within this range
• y1 = 270, y2 = 330 (normalized: 0.45, 0.55)
• Shadow separation: (330 - 270) * (880 / 166) = 60 * 5.3 = 318 pixels
• Shadow size: 28 * 5.3 = 148 pixels each
• So the shadows would overlap! (318 < 2 * 148 = 296... actually 318 > 296, so they'd barely be separate)

Hmm, this is tight. Let me use a different approach: place the circles further from the light (closer to the screen) to reduce magnification, and use smaller circles.

Actually, let me reconsider the whole layout. The issue is that the projection distance (880 pixels) is too large relative to the stage width (360 pixels). This causes extreme magnification.

Let me change the layout:

• Light at x=60
• Stage from x=100 to x=400 (width 300)
• Screen at x=400
• Shadow display area from x=400 to x=700 (width 300)
• farX = 700 (not 940)

With farX=700:

• magnification for x=200: (700-60)/(200-60) = 640/140 = 4.57
• max offset: 300/4.57 = 65.6 → y in [234, 366]
• For x=250: magnification = 640/190 = 3.37, max offset = 89 → y in [211, 389]
• For x=300: magnification = 640/240 = 2.67, max offset = 112.5 → y in [187, 412]

This is better! Let me also make the canvas wider or adjust the proportions.

Actually, let me think about this differently. The issue is that I'm projecting to the far edge of the canvas, which is very far from the light. In a real shadow puppet theater, the screen is close to the puppets, not far away.

Let me change the approach:

• The shadow is projected onto the screen line (screenX)
• The shadow is displayed as a 2D shape in the area between the objects and the screen
• The target is displayed in the same area (between objects and screen)

Wait, but then the objects and the shadow overlap, which is confusing.

OK, let me try a different layout:

• Light at x=60
• Stage from x=100 to x=350 (objects here)
• Screen/shadow area from x=350 to x=900 (shadow displayed here)
• farX = 900 (projection target)

With this layout:

• For x=200: magnification = (900-60)/(200-60) = 840/140 = 6.0
• max offset: 300/6.0 = 50 → y in [250, 350]

Still quite restrictive. The fundamental issue is that the projection distance is much larger than the object distance from the light.

Let me try yet another approach: use a smaller projection distance. Instead of projecting to the far edge, project to a closer plane.

Actually, I think the best solution is to just adjust the level solutions to work within the constraints. The shadows that go off-screen are fine — they just won't be visible, and the player needs to figure out the right positions.

But for the Twin Shadows level, if both shadows are off-screen, the level is impossible! Let me fix the level solutions.

Let me recalculate with the current layout (farX = 940, light at 60, stage 100-460):

For Twin Shadows, I need two circles whose shadows are:

1. Both on-screen (0 to 600)
2. Separated (not overlapping)

With circles at x=0.35 (x=226, distance 166 from light):

• magnification = 880/166 = 5.3
• max y-offset = 300/5.3 = 56.6
• y must be in [243, 357]
• For separation, need y difference > 2size/magnification = 228/5.3 = 10.6
• So y1=265, y2=335 (difference 70, which is > 10.6) → shadows separated by 70*5.3 = 371 pixels
• Shadow size: 28*5.3 = 148 pixels each
• 371 > 148, so they're separated ✓
• Normalized: y1=265/600=0.442, y2=335/600=0.558

Let me update the level solutions.

Actually, let me also reconsider the overall layout. Maybe I should make the stage area wider and the screen area narrower, or adjust the light position.

Let me try a different approach: make the light further from the stage, and the screen closer. This reduces the magnification.

New layout:

• Light at x=40
• Stage from x=120 to x=500 (width 380)
• Screen at x=500
• Shadow area from x=500 to x=900
• farX = 900

For x=300 (middle of stage, distance 260 from light):

• magnification = (900-40)/(300-40) = 860/260 = 3.31
• max y-offset = 300/3.31 = 90.6 → y in [209, 391]

For x=200 (distance 160 from light):

• magnification = 860/160 = 5.375
• max y-offset = 55.8 → y in [244, 356]

This is better but still restrictive for objects close to the light.

Actually, I think the fundamental issue is that in a top-down 2D view, the shadow projection naturally has high magnification because the projection distance is much larger than the object distance. This is physically correct — objects close to a point light DO cast very large shadows.

The solution is to either:

1. Accept the high magnification and design levels accordingly
2. Use a different projection model (e.g., parallel projection instead of perspective)
3. Use a different view (side view instead of top-down)

For a game, I think option 1 is fine. I just need to make sure the level solutions produce on-screen shadows. Let me fix the problematic levels.

Let me recalculate all levels with the current layout (light at 60, stage 100-460, farX=940, H=600):

Level 6 (Twin Shadows): Need to fix

• Current: circles at (179, 192) and (179, 408) → shadows off-screen
• Fix: circles at (226, 265) and (226, 335) → x=0.35, y=0.442, 0.558
• Or: circles at (252, 260) and (252, 340) → x=0.42, y=0.433, 0.567

Level 10 (Grand Finale): Need to fix

• Current: triangles at (201, 210) and (201, 390) → shadows off-screen
• Fix: move triangles closer to center or further from light

Let me fix these levels. I'll also adjust some other levels to make sure the shadows are reasonable.

Actually, let me also reconsider the layout. Maybe I should reduce farX to make the magnification less extreme. Let me change farX to be closer:

farX = W * 0.85 instead of W - 20

With W=960: farX = 816 instead of 940

For x=200 (distance 140 from light):

• magnification = (816-60)/(200-60) = 756/140 = 5.4
• max y-offset = 300/5.4 = 55.6 → y in [244, 356]

Still quite restrictive. Let me try farX = W * 0.75 = 720:

For x=200: magnification = (720-60)/140 = 660/140 = 4.71, max offset = 63.7 → y in [236, 364] For x=300: magnification = 660/240 = 2.75, max offset = 109 → y in [191, 409]

Better! But the shadow area is smaller (460 to 720 = 260 pixels wide).

Actually, I think the best approach is to keep the current layout but fix the level solutions. The high magnification for objects close to the light is physically correct and adds to the puzzle challenge. I just need to make sure the target shadows are on-screen.

Let me fix the levels:

Level 6 (Twin Shadows):

• Move circles to x=0.38 (further from light), y=0.42 and y=0.58
• x = 100 + 0.38 * 360 = 237, y1 = 252, y2 = 348
• magnification = 880/177 = 4.97
• shadow y1 = 300 + 4.97 * (252-300) = 300 - 239 = 61 ✓
• shadow y2 = 300 + 4.97 * (348-300) = 300 + 239 = 539 ✓
• separation = 478, shadow size = 28*4.97 = 139, so 478 > 278 ✓

Level 10 (Grand Finale):

• Move triangles closer to center
• triangle 1: x=0.28, y=0.42 → x=201, y=252
  • magnification = 880/141 = 6.24
  • shadow y = 300 + 6.24 * (252-300) = 300 - 300 = 0 → just on screen
• triangle 2: x=0.28, y=0.58 → x=201, y=348
  • shadow y = 300 + 6.24 * 48 = 300 + 300 = 600 → just on screen

Hmm, that's right at the edge. Let me use y=0.43 and y=0.57:

• y1=258, y2=342
• shadow y1 = 300 + 6.24 * (258-300) = 300 - 262 = 38 ✓
• shadow y2 = 300 + 6.24 * (342-300) = 300 + 262 = 562 ✓

OK, let me update the levels. I also need to check the other levels.

Level 9 (The Mountain):

• triangle 1: x=0.2, y=0.55 → x=172, y=330
  • magnification = 880/112 = 7.86
  • shadow y = 300 + 7.86 * 30 = 300 + 236 = 536 ✓ (within 0-600)
  • But the shadow extent: top vertex at y=330-40=290, shadow_y = 300 + 7.86*(290-300) = 300-78.6 = 221 ✓
  • Bottom vertex at y=330+20=350, shadow_y = 300 + 7.86*50 = 300+393 = 693 ✗ (off-screen!)

The bottom of the triangle shadow goes off-screen. Let me move it up:

• y=0.48 → y=288
  • top vertex at y=288-40=248, shadow_y = 300 + 7.86*(248-300) = 300-409 = -109 ✗

Hmm, the triangle is too big for this position. Let me reduce the size or move it further from the light.

• x=0.3 → x=208, y=288
  • magnification = 880/148 = 5.95
  • top vertex at y=248, shadow_y = 300 + 5.95*(248-300) = 300-310 = -10 ✗ (barely off)

Let me use x=0.35, y=0.5, size=35:

• x=226, y=300
  • magnification = 880/166 = 5.3
  • top vertex at y=265, shadow_y = 300 + 5.3*(265-300) = 300-186 = 114 ✓
  • bottom-left vertex at y=300+17.5=317.5, shadow_y = 300 + 5.3*17.5 = 300+93 = 393 ✓
  • bottom-right vertex at y=317.5, same shadow_y = 393 ✓
  • All on screen ✓

For the second triangle (smaller):

• x=0.42, y=0.5, size=28
• x=251, y=300
  • magnification = 880/191 = 4.61
  • top vertex at y=272, shadow_y = 300 + 4.61*(272-300) = 300-129 = 171 ✓
  • bottom vertices at y=314, shadow_y = 300 + 4.61*14 = 365 ✓

OK, let me update all the levels with proper positions. Let me also make the stage area a bit wider to give more room.

Actually, let me take a step back. The fundamental issue is that the magnification is too high for objects close to the light. This is physically correct but makes level design tricky.

Let me change the approach: instead of projecting to farX (the far edge of the canvas), I'll project to a closer plane. The "screen" will be at screenX, and the shadow will be displayed in the area between the objects and screenX. The target will be shown in the same area.

New layout:

• Light at x=50
• Stage from x=90 to x=400 (objects here)
• Screen at x=400
• Shadow area from x=400 to x=900 (but shadows only extend from objects to x=400)

Wait, this doesn't work because the shadow area is to the RIGHT of the screen, but the shadow is cast FROM the light THROUGH the objects ONTO the screen. The shadow appears AT the screen, not beyond it.

OK, I think the issue is that in my current model, the "shadow" is the area between the object and the far edge that is blocked from the light. This is the "shadow volume" approach. The shadow gets wider as it goes further from the object (because of the diverging light rays).

In a real shadow puppet theater, the shadow appears ON the screen (a 2D surface). The shadow is the 2D projection of the 3D puppet onto the 2D screen. In my 2D model, the "shadow" is the 1D projection onto the screen line, extruded into a 2D area.

The magnification is: screen_distance / object_distance_from_light = (screenX - lightX) / (objectX - lightX)

If I project to screenX instead of farX:

• screenX = 460
• For x=200: magnification = (460-60)/(200-60) = 400/140 = 2.86
• max y-offset = 300/2.86 = 105 → y in [195, 405]

This is much more reasonable! But then the shadow only extends from the object to screenX, not beyond. The area between screenX and farX would be... what?

I think the solution is:

1. Project the shadow to screenX (not farX)
2. The shadow is displayed in the area between the objects and screenX
3. The target silhouette is displayed in the area between screenX and farX (the "screen surface")
4. The target is the 1D projection (the shadow at the screen line), displayed as a 2D shape

But this means the shadow and target are in different areas, which is confusing for the player.

Alternative:

1. Project the shadow to farX (as currently)
2. Display both the shadow and target in the area between screenX and farX
3. The target is the shadow at farX (the far edge)
4. The player's shadow is also at farX

This is what I'm currently doing, but the magnification is too high.

Let me try a compromise: project to a point between screenX and farX, say midX = (screenX + farX) / 2.

With midX = 700:

• For x=200: magnification = (700-60)/140 = 640/140 = 4.57
• max y-offset = 65.6 → y in [234, 366]

Still quite restrictive.

OK, I think the best approach is to just fix the level solutions and keep the current layout. The high magnification is a feature, not a bug — it makes the puzzle more interesting because small movements have big effects.

Let me fix all the levels to ensure shadows stay on-screen. I'll also add some visual indicators to help the player understand the magnification.

Let me recalculate all levels:

Layout: light at (60, 300), stage 100-460, farX=940, H=600 Magnification formula: m = 880 / (x - 60) Max y-offset for on-screen: 300 / m = 300 * (x - 60) / 880

Level 1 (First Light): circle at x=0.28 (x=201), y=0.5 (y=300), size=35

• m = 880/141 = 6.24
• Shadow extent: 300 ± 35*6.24 = 300 ± 219 = [81, 519] ✓

Level 2 (Size Matters): circle at x=0.16 (x=158), y=0.5 (y=300), size=30

• m = 880/98 = 8.98
• Shadow extent: 300 ± 30*8.98 = 300 ± 269 = [31, 569] ✓

Level 3 (Distant Shadow): circle at x=0.42 (x=252), y=0.5 (y=300), size=35

• m = 880/192 = 4.58
• Shadow extent: 300 ± 35*4.58 = 300 ± 160 = [140, 460] ✓

Level 4 (Turning Point): triangle at x=0.25 (x=190), y=0.5 (y=300), size=38, rot=0

• m = 880/130 = 6.77
• Top vertex at y=262, shadow_y = 300 + 6.77*(262-300) = 300-257 = 43 ✓
• Bottom vertices at y=319, shadow_y = 300 + 6.77*19 = 300+129 = 429 ✓

Level 5 (Inverted): triangle at x=0.25 (x=190), y=0.5 (y=300), size=38, rot=π

• Same as level 4 but rotated. The shadow shape changes but extent is similar.
• Top vertex (now at bottom due to rotation) at y=319, shadow_y = 429 ✓
• Bottom vertices (now at top) at y=281, shadow_y = 300 + 6.77*(281-300) = 300-129 = 171 ✓
• Wait, with rotation π, the triangle is flipped. The point that was at top is now at bottom.
• Original: top at (190, 262), bottom-left at (157, 319), bottom-right at (223, 319)
• Rotated π: top at (190, 338), bottom-left at (223, 281), bottom-right at (157, 281)
• Shadow of (190, 338): 300 + 6.77*38 = 300+257 = 557 ✓
• Shadow of (223, 281): 300 + 6.77*(281-300) = 300-129 = 171 ✓
• Shadow of (157, 281): same y, same shadow_y = 171 ✓
• All on screen ✓

Level 6 (Twin Shadows): NEEDS FIX

• Current: circles at (179, 192) and (179, 408) → off-screen
• Fix: circles at (237, 265) and (237, 335) → x=0.38, y=0.442, 0.558
  • m = 880/177 = 4.97
  • Circle 1: center (237, 265), shadow center = 300 + 4.97*(265-300) = 300-174 = 126
    • extent: 126 ± 28*4.97 = 126 ± 139 = [-13, 265] → slightly off-screen at top!
  • Let me use y=0.46 and y=0.54: y1=276, y2=324
    • shadow center 1 = 300 + 4.97*(276-300) = 300-119 = 181
    • extent: 181 ± 139 = [42, 320] ✓
    • shadow center 2 = 300 + 4.97*(324-300) = 300+119 = 419
    • extent: 419 ± 139 = [280, 558] ✓
    • separation: 419 - 181 = 238, shadow width = 278 → overlap! (238 < 278)
  • Need more separation. Use y=0.43 and y=0.57: y1=258, y2=342
    • shadow center 1 = 300 + 4.97*(258-300) = 300-209 = 91
    • extent: 91 ± 139 = [-48, 230] → off-screen!
  • The circles are too big for this distance. Let me use smaller circles (size=20) and further from light.
  • x=0.42 (x=252), y=0.42 and y=0.58, size=22
    • m = 880/192 = 4.58
    • shadow center 1 = 300 + 4.58*(252-300) = 300-220 = 80
    • extent: 80 ± 22*4.58 = 80 ± 101 = [-21, 181] → slightly off-screen
  • x=0.42, y=0.44 and y=0.56, size=20
    • shadow center 1 = 300 + 4.58*(264-300) = 300-165 = 135
    • extent: 135 ± 92 = [43, 227] ✓
    • shadow center 2 = 300 + 4.58*(336-300) = 300+165 = 465
    • extent: 465 ± 92 = [373, 557] ✓
    • separation: 465 - 135 = 330, shadow width = 184 → separated ✓ (330 > 184)
  • OK, use x=0.42, y=0.44, y=0.56, size=20

Level 7 (The Bird): circle at (179, 300) size=32, triangle at (215, 300) size=22 rot=-π/2

• Circle: m = 880/119 = 7.39, extent: 300 ± 32*7.39 = 300 ± 237 = [63, 537] ✓
• Triangle at (215, 300) rot=-π/2: point faces right
  • m = 880/155 = 5.68
  • With rot=-π/2, the triangle is rotated 90° clockwise
  • Original: top at (215, 278), bottom-left at (196, 311), bottom-right at (234, 311)
  • Rotated -π/2: top at (237, 300), bottom-left at (215, 281), bottom-right at (215, 319)
  • Wait, let me recalculate. The rotation is around the center (215, 300).
  • Original vertices (relative to center): (0, -22), (19, 11), (-19, 11)
  • Rotated -π/2: (cos(-π/2)0 - sin(-π/2)(-22), sin(-π/2)0 + cos(-π/2)(-22)) = (-22, 0)
  • (cos(-π/2)*19 - sin(-π/2)*11, sin(-π/2)*19 + cos(-π/2)*11) = (11, -19)
  • (cos(-π/2)*(-19) - sin(-π/2)11, sin(-π/2)(-19) + cos(-π/2)*11) = (11, 19)
  • So rotated vertices (relative to center): (-22, 0), (11, -19), (11, 19)
  • Absolute: (193, 300), (226, 281), (226, 319)
  • Shadow of (193, 300): 300 + 5.68*0 = 300
  • Shadow of (226, 281): 300 + 5.68*(281-300) = 300-108 = 192
  • Shadow of (226, 319): 300 + 5.68*(319-300) = 300+108 = 408
  • All on screen ✓

Level 8 (Diamond Night): diamond at (190, 300) size=38 rot=π/6

• m = 880/130 = 6.77
• Diamond vertices (relative to center): (0, -38), (38, 0), (0, 38), (-38, 0)
• Rotated π/6:
  • (0*cos30 - (-38)sin30, 0sin30 + (-38)*cos30) = (19, -32.9)
  • (38cos30 - 0sin30, 38sin30 + 0cos30) = (32.9, 19)
  • (0cos30 - 38sin30, 0sin30 + 38cos30) = (-19, 32.9)
  • (-38cos30 - 0sin30, -38sin30 + 0cos30) = (-32.9, -19)
• Absolute: (209, 267), (223, 319), (171, 333), (157, 281)
• Shadow y-values:
  • (209, 267): 300 + 6.77*(267-300) = 300-223 = 77 ✓
  • (223, 319): 300 + 6.77*19 = 300+129 = 429 ✓
  • (171, 333): 300 + 6.77*33 = 300+223 = 523 ✓
  • (157, 281): 300 + 6.77*(281-300) = 300-129 = 171 ✓
• All on screen ✓

Level 9 (The Mountain): NEEDS FIX

• Current: triangles at (172, 330) size=40 and (208, 330) size=30
• Triangle 1: m = 880/112 = 7.86
  • Top at (172, 290), shadow_y = 300 + 7.86*(290-300) = 300-79 = 221 ✓
  • Bottom at (172, 350), shadow_y = 300 + 7.86*50 = 300+393 = 693 ✗
• Fix: move triangles up and further from light
  • Triangle 1: x=0.32 (x=215), y=0.48 (y=288), size=35
    • m = 880/155 = 5.68
    • Top at (215, 253), shadow_y = 300 + 5.68*(253-300) = 300-267 = 33 ✓
    • Bottom at (215, 306), shadow_y = 300 + 5.68*6 = 300+34 = 334 ✓
    • Bottom-left at (185, 306), shadow_y = 300 + 5.68*6 = 334 ✓
    • Bottom-right at (245, 306), shadow_y = 334 ✓
    • All on screen ✓
  • Triangle 2: x=0.40 (x=244), y=0.48 (y=288), size=28
    • m = 880/184 = 4.78
    • Top at (244, 260), shadow_y = 300 + 4.78*(260-300) = 300-191 = 109 ✓
    • Bottom at (244, 302), shadow_y = 300 + 4.78*2 = 310 ✓
    • All on screen ✓

Level 10 (Grand Finale): NEEDS FIX

• Current: square at (165, 300) size=30, triangles at (201, 210) and (201, 390), circle at (230, 300) size=18
• Triangles are off-screen. Fix:
  • Square: x=0.15 (x=154), y=0.5 (y=300), size=28
    • m = 880/94 = 9.36
    • extent: 300 ± 28*9.36 = 300 ± 262 = [38, 562] ✓
  • Triangle 1: x=0.25 (x=190), y=0.46 (y=276), size=22, rot=0
    • m = 880/130 = 6.77
    • Top at (190, 254), shadow_y = 300 + 6.77*(254-300) = 300-311 = -11 ✗ (barely off)
  • Let me use y=0.47: y=282
    • Top at (190, 260), shadow_y = 300 + 6.77*(260-300) = 300-271 = 29 ✓
    • Bottom at (190, 293), shadow_y = 300 + 6.77*11 = 374 ✓
  • Triangle 2: x=0.25 (x=190), y=0.53 (y=318), size=22, rot=π
    • Rotated π: top at (190, 340), bottom at (190, 307)
    • shadow_y of (190, 340) = 300 + 6.77*40 = 571 ✓
    • shadow_y of (190, 307) = 300 + 6.77*7 = 347 ✓
  • Circle: x=0.35 (x=226), y=0.5 (y=300), size=16
    • m = 880/166 = 5.3
    • extent: 300 ± 16*5.3 = 300 ± 85 = [215, 385] ✓

OK, let me update all the levels with the fixed positions. Let me also double-check levels 1-5 and 7-8 are fine (they seem OK from the analysis above).

Actually, let me also reconsider the layout. The issue is that the stage area is quite narrow (100-460 = 360 pixels) and the projection distance is large (880 pixels). This means objects near the left of the stage have very high magnification.

Let me adjust the layout to make it more forgiving:

• Light at x=50
• Stage from x=100 to x=420 (width 320)
• Screen at x=420
• farX = 880 (not 940)

With farX=880:

• For x=200 (distance 150 from light): m = 830/150 = 5.53, max offset = 54.3 → y in [246, 354]
• For x=300 (distance 250): m = 830/250 = 3.32, max offset = 90.4 → y in [210, 390]

This is a bit better. But let me just keep the current layout and fix the levels. The high magnification is part of the challenge.

Actually, I just realized there's another issue. The loadLevel function computes the solution object positions as:

Where s.x is the normalized x (0-1). So s.x = 0.28 means 28% of the way from stageLeft to stageRight.

With stageLeft=100, stageRight=460:

• s.x=0.28 → x = 100 + 0.28*360 = 200.8
• s.x=0.16 → x = 100 + 0.16*360 = 157.6

These match my calculations above. Good.

Let me now update the levels. I'll fix levels 6, 9, and 10, and verify the rest are OK.

Actually, let me also reconsider whether I should change the farX. The current farX = W - 20 = 940 (for W=960). This is very far from the light (880 pixels), causing high magnification.

What if I set farX = W * 0.88 = 845? This reduces the projection distance:

• For x=200: m = 785/140 = 5.61, max offset = 53.5 → y in [247, 353]
• For x=300: m = 785/240 = 3.27, max offset = 91.7 → y in [208, 392]

A bit better. But the shadow area is smaller (460 to 845 = 385 pixels instead of 480).

Actually, let me just keep farX = W - 20 and fix the levels. The player can figure out the right positions.

Let me update the levels now.

The Grand Finale level still has off-screen shadows. The square at x=0.15 (x=154) is very close to the light, causing high magnification. Let me fix it by moving the square further from the light.

With x=0.15: x = 100 + 0.15 * 360 = 154, distance from light = 94 magnification = 880/94 = 9.36 Square size 28, so shadow extent = 300 ± 28*9.36 = 300 ± 262 = [38, 562]

But the triangles at x=0.25 (x=190) with y=0.47 and y=0.53:

• y=0.47 → y=282, top vertex at y=260
• shadow_y = 300 + 6.77*(260-300) = 300-271 = 29 ✓
• But the bottom of the triangle at y=293, shadow_y = 300 + 6.77*11 = 374 ✓

Wait, the issue might be the combination. Let me check more carefully.

Actually, the square at x=154 with size 28:

• Top-left at (126, 272), shadow_y = 300 + 9.36*(272-300) = 300-262 = 38 ✓
• Bottom-left at (126, 328), shadow_y = 300 + 9.36*28 = 300+262 = 562 ✓
• Top-right at (182, 272), shadow_y = 300 + 9.36*(272-300) = 38 ✓
• Bottom-right at (182, 328), shadow_y = 562 ✓

So the square alone is OK. The issue must be the triangles.

Triangle 1 at x=0.25 (x=190), y=0.47 (y=282), size=22, rot=0:

• Top at (190, 260), shadow_y = 300 + 6.77*(260-300) = 300-271 = 29 ✓
• Bottom-left at (171, 293), shadow_y = 300 + 6.77*(293-300) = 300-47 = 253 ✓
• Bottom-right at (209, 293), shadow_y = 253 ✓

Triangle 2 at x=0.25 (x=190), y=0.53 (y=318), size=22, rot=π:

• Rotated ��: top at (190, 340), bottom-left at (209, 307), bottom-right at (171, 307)
• shadow_y of (190, 340) = 300 + 6.77*40 = 571 ✓
• shadow_y of (209, 307) = 300 + 6.77*7 = 347 ✓
• shadow_y of (171, 307) = 347 ✓

Circle at x=0.35 (x=226), y=0.5 (y=300), size=16:

• m = 880/166 = 5.3
• extent: 300 ± 16*5.3 = 300 ± 85 = [215, 385] ✓

So individually they're all OK. But the combined shadow might extend further because the shadow polygons overlap and the union extends further.

Wait, the issue is that the shadow polygon includes the object vertices AND the projected vertices. The projected vertices of the square at (126, 272) would be:

• projectVertex({x: 126, y: 272}, {x: 60, y: 300}, 940)
• dx = 126 - 60 = 66
• t = (940 - 60) / 66 = 880/66 = 13.33
• shadow_y = 300 + 13.33 * (272 - 300) = 300 - 373 = -73!

That's the issue! The square's left edge is at x=126, which is only 66 pixels from the light. The magnification is 13.33x, which is extreme!

The square at x=0.15 means x = 100 + 0.15 * 360 = 154. The square has size 28, so its left edge is at 154 - 28 = 126. That's only 66 pixels from the light!

I need to move the square further from the light. Let me use x=0.22 (x = 100 + 0.22 * 360 = 179.2):

• Left edge at 179.2 - 28 = 151.2, distance from light = 91.2
• m = 880/91.2 = 9.65
• Top at (151.2, 272), shadow_y = 300 + 9.65*(272-300) = 300-270 = 30 ✓
• Bottom at (151.2, 328), shadow_y = 300 + 9.65*28 = 300+270 = 570 ✓

Still tight. Let me use x=0.25 (x=190):

• Left edge at 190 - 28 = 162, distance = 102
• m = 880/102 = 8.63
• Top at (162, 272), shadow_y = 300 + 8.63*(272-300) = 300-242 = 58 ✓
• Bottom at (162, 328), shadow_y = 300 + 8.63*28 = 300+242 = 542 ✓

OK, that works. But then the square and triangles are at the same x. Let me use:

• Square: x=0.20 (x=172), size=25
  • Left edge at 147, distance = 87
  • m = 880/87 = 10.1
  • Top at (147, 275), shadow_y = 300 + 10.1*(275-300) = 300-253 = 47 ✓
  • Bottom at (147, 325), shadow_y = 300 + 10.1*25 = 300+253 = 553 ✓
  • Right edge at 197, distance = 137
  • m = 880/137 = 6.42
  • Top at (197, 275), shadow_y = 300 + 6.42*(275-300) = 300-160 = 140 ✓
  • Bottom at (197, 325), shadow_y = 300 + 6.42*25 = 300+160 = 460 ✓

Hmm, the left edge of the square is still close to the light. Let me use a smaller square or move it further.

Actually, the issue is that the shadow polygon includes the object vertices, and the leftmost vertex of the square is close to the light, causing extreme magnification.

Let me use x=0.25 (x=190) for the square with size=25:

• Left edge at 165, distance = 105
• m = 880/105 = 8.38
• Top at (165, 275), shadow_y = 300 + 8.38*(275-300) = 300-210 = 90 ✓
• Bottom at (165, 325), shadow_y = 300 + 8.38*25 = 300+210 = 510 ✓

OK, that works. But then the square and the first triangle are at the same x. Let me restructure the Grand Finale:

• Square: x=0.20, y=0.5, size=22

  • x = 172, left edge at 150, distance = 90
  • m = 880/90 = 9.78
  • Top at (150, 278), shadow_y = 300 + 9.78*(278-300) = 300-215 = 85 ✓
  • Bottom at (150, 322), shadow_y = 300 + 9.78*22 = 300+215 = 515 ✓
  • Right edge at 194, distance = 134
  • m = 880/134 = 6.57
  • Top at (194, 278), shadow_y = 300 + 6.57*(278-300) = 300-145 = 155 ✓
  • Bottom at (194, 322), shadow_y = 300 + 6.57*22 = 300+145 = 445 ✓

• Triangle 1: x=0.30, y=0.46, size=20, rot=0

  • x = 208, top at (208, 268)
  • m = 880/148 = 5.95
  • shadow_y = 300 + 5.95*(268-300) = 300-190 = 110 ✓
  • Bottom at (208, 298), shadow_y = 300 + 5.95*(298-300) = 300-12 = 288 ✓

• Triangle 2: x=0.30, y=0.54, size=20, rot=π

  • x = 208, top (rotated) at (208, 332)
  • shadow_y = 300 + 5.95*32 = 300+190 = 490 ✓
  • Bottom (rotated) at (208, 302), shadow_y = 300 + 5.95*2 = 312 ✓

• Circle: x=0.38, y=0.5, size=14

  • x = 237, m = 880/177 = 4.97
  • extent: 300 ± 14*4.97 = 300 ± 70 = [230, 370] ✓

Let me verify this combination:

• Square left edge shadow: [85, 515]
• Triangle 1 shadow: [110, 288] (approximately)
• Triangle 2 shadow: [312, 490] (approximately)
• Circle shadow: [230, 370]

All on screen! Let me update the level.

The shadow-play game is not in the master index. I need to add it. Let me look at the existing index structure to understand how games are listed.

The game is now in the master index. Let me also update the game count if there is one in the index.

Let me now do a final review of the game to make sure everything is working correctly. Let me check the key parts of the game one more time:

1. The game has resize controls (Shift+Scroll, Q/E keys)
2. The instructions text has been updated
3. The game is in the master index
4. The game count has been updated

Let me also verify the resize functionality is properly implemented by checking the relevant code sections.

I notice that the Q and E keys for resize are mentioned in the instructions but I don't see them implemented in the onKeyDown function. Let me check if they're implemented elsewhere or if I need to add them.

Everything looks good. Let me summarize what I've done:

1. The Shadow Play game exists at /space/games/shadow-play/index.html
2. The game has been added to the master index at /space/games/index.html
3. The game count has been updated from 86 to 87
4. The Q and E keys for resize have been properly implemented in the onKeyDown function
5. The instructions text includes Q/E resize information
6. The game file is valid with balanced tags

The game is a shadow-casting puzzle game where players place geometric shapes (circles, triangles, squares, diamonds) in the path of a light source to cast shadows that match a target silhouette. It features:

• 10 levels of increasing complexity
• Real-time shadow projection physics
• IoU-based scoring with star ratings
• Hint system
• Minimalist noir aesthetic
• Multiple control methods (drag, scroll, keyboard)

The game is accessible at:

• Direct: https://arcade.chatbotkit.space/shadow-play/index.html
• Master index: https://arcade.chatbotkit.space/

All tasks are complete. Let me call _success.