Lecture 7: Intro to Geometry, Splines, and Bezier Curves (110)

SeanW0823

The Bezier surfaces shown in class are mostly rectangles stretched into smooth surfaces. How does the math extend to triangular meshes in the "Gumbo" model?

jacklishufan

So as is covered in the lecture, the Bezier surface essential give a continuous map from (u,v) to three-dimensional space (x,y,z). So it can map arbitrary structures from the 2D-Plane (including triangles)

ClaireLiu123

I looked up that Bézier surface is a representation of such polynomial pieces which makes their interactive design easier and more intuitive than with other representations. Also, I saw there is a Nurb curve that's different from Bézier that doesn't touch the control points, they just bend towards them. But Bézier curve control over tangents and the curve always touches the control point.

The Bezier surfaces shown in class are mostly rectangles stretched into smooth surfaces. How does the math extend to triangular meshes in the "Gumbo" model?

So as is covered in the lecture, the Bezier surface essential give a continuous map from (u,v) to three-dimensional space (x,y,z). So it can map arbitrary structures from the 2D-Plane (including triangles)

I looked up that Bézier surface is a representation of such polynomial pieces which makes their interactive design easier and more intuitive than with other representations. Also, I saw there is a Nurb curve that's different from Bézier that doesn't touch the control points, they just bend towards them. But Bézier curve control over tangents and the curve always touches the control point.