Drawing triangles using linear interpolation between vertices.
- Author
- Sukesh Ashok Kumar
This example demonstrates how to draw a triangle by connecting three points (vertices) with straight lines. It introduces polygon concepts and shows how to calculate points along a line using linear interpolation.
Mathematical Concepts:
- Triangle: polygon with 3 vertices and 3 sides
- Vertices: corner points that define the triangle
- Linear interpolation: finding intermediate points between two endpoints
- Point-slope form: (y - y1) / (y2 - y1) = (x - x1) / (x2 - x1)
- Rearranged: y = y1 + (y2 - y1) × (x - x1) / (x2 - x1)
Triangle Properties:
- Sum of interior angles = 180°
- 3 sides, 3 vertices, 3 angles
- Simplest polygon
- This example creates an isosceles triangle (two equal sides)
Programming Concepts:
- Linear interpolation (lerp) for line drawing
- Connecting points to form polygons
- Forward and backward iteration (x++ vs x–)
- Integer division for coordinate calculation
- Breaking complex shapes into simple lines
What you'll learn:
- How to define a triangle using three vertices
- Drawing lines by interpolating between endpoints
- The mathematical formula for points on a line segment
- Why we need different loop directions for different lines
- Basic polygon construction
- Converting mathematical concepts to pixel coordinates
Line Drawing Algorithm: For a line from (x1,y1) to (x2,y2):
- Iterate x from x1 to x2
- For each x, calculate y using linear interpolation
- Formula: y = y1 + (y2-y1) × (x-x1) / (x2-x1)
- This creates a straight line between the two points
Why Different Loop Directions?
- Line 1 (top to bottom-left): x decreases (x–)
- Line 2 (bottom-left to bottom-right): x increases (x++)
- Line 3 (bottom-right to top): x decreases (x–) We loop in the direction where x changes monotonically.
Compile:
gcc m-triangle.c gfx/simplegfx.c -o output/m-triangle -lX11
Run:
1.9.1