Computer Graphics: Difference between revisions

From Adam Colton
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   p2 = Line( l1(t1), l2(t1 )(t0)
   p2 = Line( l1(t1), l2(t1 )(t0)
and this works if there are more lines and more parametric points. The order of the points does not matter.
and this works if there are more lines and more parametric points. The order of the points does not matter.
6.1 Covers degree elevation for Bezier curves; how to take n points that define a curve and find n+1 points that define the same curve.

Revision as of 15:10, 29 April 2019

I'm leaving this as is, but really my interest is "Computational Geometry"

Notes

BCS

  • Flat shading
  • Gouraud Shading
  • Phong Shading

Catmull-Clark Surface

Curves and Surfaces for CAGD

Resume: 58

CAGD: computer aided geometric design

www.mkp.com/cagd5e

Interesting solution to a type problem I've had; points cannot be directly added to points. But, say finding the center of a triangle, it's (t[0]+t[1]+t[2])/3. The solution is that affine combination of points is allowed.

A line can also be thought of as an affine map

 F(t) = (1-t)t0 + (t)t1

Menelaos' Theorem:

 given l1, l2
 p1 = Line( l1(t0), l2(t0 )(t1)
 p2 = Line( l1(t1), l2(t1 )(t0)

and this works if there are more lines and more parametric points. The order of the points does not matter.

6.1 Covers degree elevation for Bezier curves; how to take n points that define a curve and find n+1 points that define the same curve.