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How to map points onto quadrilaterals using variables in Scratch

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GD

GeometryDev_Alex

Posted on July 21, 2025 • Advanced

📐 Need help with coordinate mapping project

Hey everyone! I’m working on a geometric transformation project where I need to map coordinate points onto a quadrilateral shape. I’ve set up variables for the coordinates, but they’re not properly mapping the points onto the quad as expected.

The issue is that my variables don’t seem to be correctly transforming the input coordinates to match the quadrilateral’s geometry. I think there might be something wrong with my transformation matrix or coordinate system setup.

Has anyone worked with point-to-quad mapping before? I need the points to properly project onto the quadrilateral surface! 🔢

MT

MathTransform_Pro

Replied 2 hours later • ⭐ Best Answer

Great question @GeometryDev_Alex! Point-to-quadrilateral mapping is a complex geometric transformation. Let me break down the solution step by step:

🎯 Understanding Quadrilateral Mapping

Here’s the mathematical concept behind mapping points to a quad:

flowchart TD A[📍 Input Point (x, y)] --> B[🔄 Bilinear Interpolation] B --> C[📐 Quadrilateral Coordinates] D[🔢 Quad Corner Points] --> E[📊 Transformation Matrix] E --> F[🎯 Mapped Output Point] G[⚠️ Key Components] --> H[Corner coordinates (x1,y1) to (x4,y4)] G --> I[Interpolation parameters (u, v)] G --> J[Bilinear transformation formula] style A fill:#e3f2fd style C fill:#e8f5e8 style F fill:#fff3e0 style G fill:#ffebee

🔧 Solution 1: Basic Bilinear Mapping

First, let’s set up the fundamental mapping system:

    // Define quadrilateral corner points
when flag clicked
set [quad x1 v] to [-100]  // Top-left corner
set [quad y1 v] to [100]
set [quad x2 v] to [150]   // Top-right corner
set [quad y2 v] to [120]
set [quad x3 v] to [100]   // Bottom-right corner
set [quad y3 v] to [-80]
set [quad x4 v] to [-120]  // Bottom-left corner
set [quad y4 v] to [-100]

// Input coordinates (normalized 0-1)
set [input u v] to [0.5]   // Horizontal parameter
set [input v v] to [0.3]   // Vertical parameter

map point to quad

🧮 Solution 2: Bilinear Interpolation Function

Implement the core mapping algorithm:

    define map point to quad
// Calculate intermediate points for bilinear interpolation

// Top edge interpolation
set [top x v] to (((quad x1) * ((1) - (input u))) + ((quad x2) * (input u)))
set [top y v] to (((quad y1) * ((1) - (input u))) + ((quad y2) * (input u)))

// Bottom edge interpolation
set [bottom x v] to (((quad x4) * ((1) - (input u))) + ((quad x3) * (input u)))
set [bottom y v] to (((quad y4) * ((1) - (input u))) + ((quad y3) * (input u)))

// Final point interpolation
set [mapped x v] to (((top x) * ((1) - (input v))) + ((bottom x) * (input v)))
set [mapped y v] to (((top y) * ((1) - (input v))) + ((bottom y) * (input v)))

// Move sprite to mapped position
go to x: (mapped x) y: (mapped y)
stamp

🎨 Solution 3: Interactive Mapping System

Create a system that responds to mouse input:

    when flag clicked
forever
// Convert mouse position to normalized coordinates
set [mouse u v] to (((mouse x) + (240)) / (480))  // Normalize to 0-1
set [mouse v v] to (((mouse y) + (180)) / (360))  // Normalize to 0-1

// Clamp values to valid range
if <(mouse u) < [0]> then
set [mouse u v] to [0]
end
if <(mouse u) > [1]> then
set [mouse u v] to [1]
end
if <(mouse v) < [0]> then
set [mouse v v] to [0]
end
if <(mouse v) > [1]> then
set [mouse v v] to [1]
end

// Map mouse position to quadrilateral
set [input u v] to (mouse u)
set [input v v] to (mouse v)
map point to quad
end

🚀 Solution 4: Advanced Perspective Mapping

For more realistic perspective transformations:

    define perspective map (source_x) (source_y)
// Advanced perspective transformation with depth

// Calculate perspective weights
set [w1 v] to (((1) - (source_x)) * ((1) - (source_y)))
set [w2 v] to ((source_x) * ((1) - (source_y)))
set [w3 v] to ((source_x) * (source_y))
set [w4 v] to (((1) - (source_x)) * (source_y))

// Apply perspective correction
set [total_weight v] to (((w1) + (w2)) + ((w3) + (w4)))

// Calculate weighted coordinates
set [weighted_x v] to ((((w1) * (quad x1)) + ((w2) * (quad x2))) + (((w3) * (quad x3)) + ((w4) * (quad x4))))
set [weighted_y v] to ((((w1) * (quad y1)) + ((w2) * (quad y2))) + (((w3) * (quad y3)) + ((w4) * (quad y4))))

// Final perspective-corrected position
set [final x v] to ((weighted_x) / (total_weight))
set [final y v] to ((weighted_y) / (total_weight))

go to x: (final x) y: (final y)

🔍 Solution 5: Debugging and Visualization

Add visual debugging to understand the mapping:

    define draw quad outline
// Draw quadrilateral outline for visualization
pen up
go to x: (quad x1) y: (quad y1)
pen down
set pen color to [#ff0000]
set pen size to [3]

// Draw quad edges
go to x: (quad x2) y: (quad y2)
go to x: (quad x3) y: (quad y3)
go to x: (quad x4) y: (quad y4)
go to x: (quad x1) y: (quad y1)
pen up

define draw grid points
// Draw a grid of mapped points
set [grid_u v] to [0]
repeat [11]
set [grid_v v] to [0]
repeat [11]
set [input u v] to (grid_u)
set [input v v] to (grid_v)
map point to quad

// Draw point
set pen color to [#0000ff]
set pen size to [5]
pen down
pen up

change [grid_v v] by [0.1]
end
change [grid_u v] by [0.1]
end

💡 Pro Tips for Quad Mapping

Here are some advanced techniques:

Texture Mapping:

    define map texture (texture_u) (texture_v)
// Map texture coordinates to quad surface
set [input u v] to (texture_u)
set [input v v] to (texture_v)
map point to quad

// Switch to appropriate texture costume
set [costume_index v] to (((texture_u) * (10)) + ((texture_v) * (100)))
switch costume to (costume_index)
stamp

Inverse Mapping:

    define find uv from point (target_x) (target_y)
// Find UV coordinates for a given world point (approximate)
set [best_u v] to [0.5]
set [best_v v] to [0.5]
set [best_distance v] to [999999]

set [test_u v] to [0]
repeat [21]  // Test 21 points across U
set [test_v v] to [0]
repeat [21]  // Test 21 points across V
set [input u v] to (test_u)
set [input v v] to (test_v)
map point to quad

// Calculate distance to target
set [distance v] to (sqrt of (((((mapped x) - (target_x)) * ((mapped x) - (target_x))) + (((mapped y) - (target_y)) * ((mapped y) - (target_y))))))

if <(distance) < (best_distance)> then
set [best_distance v] to (distance)
set [best_u v] to (test_u)
set [best_v v] to (test_v)
end

change [test_v v] by [0.05]
end
change [test_u v] by [0.05]
end

// Return best UV coordinates
set [result u v] to (best_u)
set [result v v] to (best_v)

The key is understanding that bilinear interpolation creates smooth transitions between the four corner points of your quadrilateral! 📐

GD

GeometryDev_Alex

Replied 1 hour later

@MathTransform_Pro This is absolutely incredible! Thank you so much! 🎉

The bilinear interpolation approach worked perfectly. I was missing the proper edge interpolation step - I was trying to directly map coordinates without the intermediate calculations. Your debugging visualization also helped me see exactly what was happening.

One question: how would I handle non-convex quadrilaterals? Do I need a different approach?

MT

MathTransform_Pro

Replied 30 minutes later

@GeometryDev_Alex Great question about non-convex quads! 🤔

For non-convex (concave) quadrilaterals, bilinear interpolation can create unexpected results because the mapping might “fold” on itself. Here are two approaches:

1. Triangle-based mapping: Split the quad into two triangles and use barycentric coordinates for each triangle.

2. Constraint checking: Add validation to ensure your quad remains convex:

    define check quad convexity
// Check if quadrilateral is convex using cross products
set [convex v] to [true]

// Calculate cross products for each edge
set [cross1 v] to ((((quad x2) - (quad x1)) * ((quad y4) - (quad y1))) - (((quad y2) - (quad y1)) * ((quad x4) - (quad x1))))
set [cross2 v] to ((((quad x3) - (quad x2)) * ((quad y1) - (quad y2))) - (((quad y3) - (quad y2)) * ((quad x1) - (quad x2))))

if <<(cross1) > [0]> and <(cross2) < [0]>> then
set [convex v] to [false]
end
if <<(cross1) < [0]> and <(cross2) > [0]>> then
set [convex v] to [false]
end

For most applications, keeping your quad convex will give the best results! 📐

VB

Vibelf_Community

Pinned Message • Moderator

📐 Ready to Master Advanced Geometry Programming?

Excellent discussion on coordinate transformations! For those looking to create even more sophisticated mathematical projects, our community can help you implement:

  • 🔢 Complex geometric transformations
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