CS 552 Computer Graphics Lecture 23 Surface Representation

CS 552: Computer Graphics Lecture 23: Surface Representation

Recap • Curves • Cubic spline • Bezier • B spline

Objective After completing this lecture, students will be able to o Mathematically represent a surface patches Ø Planar Surface Ø Curved Surface Ø Bi-linear Surface Ø Lofted or Ruled Surface o Solve related mathematical problems

Surface • Representation of surface o Explicit o Implicit o Parametric

A Surface Patch Boundary curves

Displaying a Surface Patch • A surface patch can be displayed either as a wire frame

Plane Surfaces • It is possible to express points which fall on a surface in terms of two parameters (u, v) • Boundary conditions are to be specified • The derivatives of the point functions are ? • In matrix form? • Represents differential change in the uv-plane to the corresponding differential change in the xy-plane.

Example •

Curved Surface Representation • A curve is represented as a vector valued function of a single variable • A surface is represented by a bivariate vector-valued function • How to represent a curve on the surface? • How a point on the surface may be represented?

Bilinear Surfaces • One of the simplest surfaces is the bilinear surface. • Four comer points of the surface are given in the u, v-plane o P(0, 0) o P(0, 1) o P(1, 0) o P(1, 1) • Expression for the parametric surface?

Lofted or Ruled Surfaces •

Example •

Linear Coons Surface •

Example

Thank you Next Lecture: Surface representation