Computer Graphics

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

• Broken Chalk Series This is excellent
• Graphics Gems books
• https://www.reddit.com/r/GraphicsProgramming/
• https://www.reddit.com/r/raytracing/
• https://github.com/hunterloftis/oneweekend/blob/master/readme.md
• Ray Tracing in a Weekend
• [1]

Notes

BCS

• Flat shading
• Gouraud Shading
• Phong Shading

Catmull-Clark Surface

Curves and Surfaces for CAGD

Resume: 96

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.

6.4 Covers degree reduction; given n points, produce the closes possible curve with n-1 points.

B-spline

https://en.wikipedia.org/wiki/B-spline

Basis Spline

• Joins many low degree Bezier curves

A k degree B-spline deined by n control points will have n-k Bezier curves. So a cubic (k=3) B-spline with 6 control points will have n-k = 6-3 = 3 Bezier curves.