Editable Cubic Bézier Surface

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2016-06-17 05:22

This example demonstrates an editable cubic Bézier surface. Key mathematical concepts include polynomial functions, equations, and geometric transformations. Using GeoGebra commands such as If, Surface, and Segment, complex surface shapes can be constructed. Suitable for high school and above students or teachers for teaching or research on geometric transformations and surface construction.

GeoGebra Commands & Parameters

If(wc, 3, 2) → n
Surface(((b_{30}(u) * b_{30}(v)) * A1) + ((b_{31}(u) * b_{30}(v)) * A2) + ((b_{32}(u) * b_{30}(v)) * A3) + ((b_{33}(u) * b_{30}(v)) * A4) + ((b_{30}(u) * b_{31}(v)) * B1) + ((b_{31}(u) * b_{31}(v)) * B2) + ((b_{32}(u) * b_{31}(v)) * B3) + ((b_{33}(u) * b_{31}(v)) * B4) + ((b_{30}(u) * b_{32}(v)) * C1) + ((b_{31}(u) * b_{32}(v)) * C2) + ((b_{32}(u) * b_{32}(v)) * C3) + ((b_{33}(u) * b_{32}(v)) * C4) + ((b_{30}(u) * b_{33}(v)) * D1) + ((b_{31}(u) * b_{33}(v)) * D2) + ((b_{32}(u) * b_{33}(v)) * D3) + ((b_{33}(u) * b_{33}(v)) * D4), u, 0, 1, v, 0, 1) → S_3
Segment(A1, A4) → sx
Segment(A1, D1) → sy

AI Drawing Prompt Reference

Create an editable cubic Bézier surface to demonstrate key mathematical concepts like polynomial functions, equations, and geometric transformations. Start by constructing the four vertices of the surface, then connect these vertices to form the boundary line segments, and finally generate the complete cubic Bézier surface using the vertices and line segments to visualize its construction and geometric properties.

The prompt above was compiled from the original drawing commands and is for reference only.