Bezier Surface by Jacky Lu
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This example demonstrates the construction of a Bezier surface. It involves concepts of polynomial functions and random variables. Using the Surface command, it constructs a surface with points A to P and plane a. Suitable for high school or university-level solid geometry and calculus courses.
GeoGebra Commands & Parameters
Surface(((1 - s)^(3) * ((x(A) * (1 - t)^(3)) + (((x(B) * 3) * t) * (1 - t)^(2)) + (((x(C) * 3) * t^(2)) * (1 - t)) + (x(D) * t^(3)))) + (((3 * s) * (1 - s)^(2)) * ((x(E) * (1 - t)^(3)) + (((x(F) * 3) * t) * (1 - t)^(2)) + (((x(G) * 3) * t^(2)) * (1 - t)) + (x(H) * t^(3)))) + (((3 * s^(2)) * (1 - s)) * ((x(I) * (1 - t)^(3)) + (((x(J) * 3) * t) * (1 - t)^(2)) + (((x(K) * 3) * t^(2)) * (1 - t)) + (x(L) * t^(3)))) + (s^(3) * ((x(M) * (1 - t)^(3)) + (((x(N) * 3) * t) * (1 - t)^(2)) + (((x(O) * 3) * t^(2)) * (1 - t)) + (x(P) * t^(3)))), ((1 - s)^(3) * ((y(A) * (1 - t)^(3)) + (((y(B) * 3) * t) * (1 - t)^(2)) + (((y(C) * 3) * t^(2)) * (1 - t)) + (y(D) * t^(3)))) + (((3 * s) * (1 - s)^(2)) * ((y(E) * (1 - t)^(3)) + (((y(F) * 3) * t) * (1 - t)^(2)) + (((y(G) * 3) * t^(2)) * (1 - t)) + (y(H) * t^(3)))) + (((3 * s^(2)) * (1 - s)) * ((y(I) * (1 - t)^(3)) + (((y(J) * 3) * t) * (1 - t)^(2)) + (((y(K) * 3) * t^(2)) * (1 - t)) + (y(L) * t^(3)))) + (s^(3) * ((y(M) * (1 - t)^(3)) + (((y(N) * 3) * t) * (1 - t)^(2)) + (((y(O) * 3) * t^(2)) * (1 - t)) + (y(P) * t^(3)))), ((1 - s)^(3) * ((z(A) * (1 - t)^(3)) + (((z(B) * 3) * t) * (1 - t)^(2)) + (((z(C) * 3) * t^(2)) * (1 - t)) + (z(D) * t^(3)))) + (((3 * s) * (1 - s)^(2)) * ((z(E) * (1 - t)^(3)) + (((z(F) * 3) * t) * (1 - t)^(2)) + (((z(G) * 3) * t^(2)) * (1 - t)) + (z(H) * t^(3)))) + (((3 * s^(2)) * (1 - s)) * ((z(I) * (1 - t)^(3)) + (((z(J) * 3) * t) * (1 - t)^(2)) + (((z(K) * 3) * t^(2)) * (1 - t)) + (z(L) * t^(3)))) + (s^(3) * ((z(M) * (1 - t)^(3)) + (((z(N) * 3) * t) * (1 - t)^(2)) + (((z(O) * 3) * t^(2)) * (1 - t)) + (z(P) * t^(3)))), s, 0, 1, t, 0, 1) → a
AI Drawing Prompt Reference
Create a Bezier surface defined by points A to P, which is constructed from four cubic polynomial functions along the s and t directions. First, define points A to P, then use the Surface command with the x, y, and z coordinates of these points as parameters to construct a 3D surface a.
The prompt above was compiled from the original drawing commands and is for reference only.