**deCasteljau Revisited Barycentrically:**-
- Linear blend expressed in barycentric terms
- Higher powers and a symmetric form of the Bernstein polynomials:
- Examples

- Linear blend expressed in barycentric terms
**Surfaces - Barycentric Blends on Triangles:**-
- Formulas:

- Formulas:
**Triangular deCasteljau:**-
- Join adjacently indexed by triangles
- Find
*r*:*s*:*t*barycentric point in each triangle - Join adjacent points by triangles
- Repeat
- Final point is the surface point
*P*(*r*,*s*,*t*) - Final triangle is tangent to the surface at
*P*(*r*,*s*,*t*)

- Final point is the surface point
- Triangle up/down schemes become tretrahedral up/down schemes

**Properties:**-
- Each boundary curve is a Bézier curve
- Patches will be joined smoothly if pairs of boundary triangles are affine images of domain triangles

CS488/688: Introduction to Interactive Computer Graphics

University of Waterloo

Computer Graphics Lab