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de Casteljau's Algorithm Demo

de Casteljau's Algorithm Demo
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2018-04-04 00:14
FunctionMatrixTransformationGeometric ConstructionLocus
In collections Mathematics of Computer Graphics
This example dynamically demonstrates de Casteljau's algorithm for Bezier curve division, visually linking the curve to control points. Core math concepts include Bezier curves, matrix operations, linear algebra, and geometric transformations. GeoGebra commands like Segment and Locus are used to construct control points, intermediate points, and animation trajectories. Suitable for high school and above learners to understand parametric curves and geometric algorithms.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(C, B) → b
  3. Segment(C, D) → c
  4. Segment(D, E) → d
  5. Segment(A_t, B_t) → e
  6. Segment(B_t, C_t) → f
  7. Segment(C_t, D_t) → g
  8. Segment(AB_t, BC_t) → h
  9. Segment(BC_t, CD_t) → i
  10. Segment(ABC_t, BCD_t) → j
  11. Locus(ABCD_t, t) → loc1
  12. Locus(P3, t) → loc2
  13. Locus(P2, t) → loc3
  14. Segment(A, B) → p

AI Drawing Prompt Reference

Draw a dynamic demonstration of de Casteljau's algorithm for Bezier curve division, showing how the curve connects to control points, including control points, intermediate points, and animation trajectories, reflecting matrix operations, linear algebra, and geometric transformations. Start by drawing initial control points and lines, then animate intermediate points to form the curve.
The prompt above was compiled from the original drawing commands and is for reference only.