Computer Graphics: Difference between revisions
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I'm leaving this as is, but really my interest is "Computational Geometry" | |||
* [https://www.youtube.com/watch?v=Is6D5rnWEvs&list=PL_w_qWAQZtAZhtzPI5pkAtcUVgmzdAP8g Broken Chalk Series] This is excellent | * [https://www.youtube.com/watch?v=Is6D5rnWEvs&list=PL_w_qWAQZtAZhtzPI5pkAtcUVgmzdAP8g Broken Chalk Series] This is excellent | ||
* Graphics Gems books | * Graphics Gems books | ||
* https://www.reddit.com/r/GraphicsProgramming/ | |||
* https://www.reddit.com/r/raytracing/ | |||
* https://github.com/hunterloftis/oneweekend/blob/master/readme.md | |||
* [https://drive.google.com/drive/folders/14yayBb9XiL16lmuhbYhhvea8mKUUK77W Ray Tracing in a Weekend] | |||
* [http://graphics.cs.ucdavis.edu/~joy/GeometricModelingLectures/] | |||
== Notes == | == Notes == | ||
=== | === BCS === | ||
* Flat shading | * Flat shading | ||
* Gouraud Shading | * Gouraud Shading | ||
* Phong Shading | * Phong Shading | ||
Catmull-Clark Surface | |||
== B-spline == | |||
* https://en.wikipedia.org/wiki/B-spline | |||
* https://www.youtube.com/watch?v=r6UcF0S0HvQ&t=2s | |||
Basis Spline; a curve defined by control points and a knot vector. | |||
* 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. | |||
* C<sup>0</sup> continuity means that the last point on each Bezier curve is the same as the first point on the next - there are no gaps. | |||
* C<sup>1</sup> the derivatives of the curves are continuous | |||
* C<sup>2</sup> the second derivatives of the curves are continuous | |||
The length of the knot vector is m=k+n. For a uniform knot vector (most common), the numbers will be integers increasing by one, so m=5 will be T=(0,1,2,3,4). | |||
S(t) = ∑<sub>i</sub><sup>n</sup>N<sub>i,k</sub>(t)P<sub>i</sub> | |||
N<sub>i,0</sub>(t) = (t<sub>i</sub> <= t < t<sub>i+1</sub) ? 1 : 0 | |||
N<sub>i,j</sub>(t) = (t - t<sub>i</sub>)/(t<sub>i+j</sub> - t<sub>i</sub>)N<sub>i,j-1</sub>(t) + (t<sub>i+j+1</sub> - t)/(t<sub>i+j+1</sub> - t<sub>i+1</sub>)N<sub>i+1,j-1</sub>(t) | |||
This forms a triangle because each N where j!= is dependent on two N where j is one less. And the curve itself is the case where i=0 j=n. The ternary acts like a switch that turns on one N where j=0. | |||
[[Category:Computer Graphics]] | |||
Latest revision as of 14:02, 28 August 2019
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
B-spline
Basis Spline; a curve defined by control points and a knot vector.
- 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.
- C0 continuity means that the last point on each Bezier curve is the same as the first point on the next - there are no gaps.
- C1 the derivatives of the curves are continuous
- C2 the second derivatives of the curves are continuous
The length of the knot vector is m=k+n. For a uniform knot vector (most common), the numbers will be integers increasing by one, so m=5 will be T=(0,1,2,3,4).
S(t) = ∑inNi,k(t)Pi Ni,0(t) = (ti <= t < ti+1</sub) ? 1 : 0 Ni,j(t) = (t - ti)/(ti+j - ti)Ni,j-1(t) + (ti+j+1 - t)/(ti+j+1 - ti+1)Ni+1,j-1(t)
This forms a triangle because each N where j!= is dependent on two N where j is one less. And the curve itself is the case where i=0 j=n. The ternary acts like a switch that turns on one N where j=0.