Category: KnowHow

3D Object Intersection

3차원 객체들의 교차(혹은 충돌)여부를 검사하는 것은 그래픽관련 프로그래밍할 때, 매우 빈번하게 접하는 문제이다.
이런 문제들을 한 자리에 일목요연하게 정리한 웹페이지이다.
위치 : http://www.realtimerendering.com/int/
자체 설명
This page gives a grid of intersection routines for various popular
objects, pointing to resources
in books and on the web. For a unified static and dynamic object
intersection and distance library (non-commercial use only, though),
see
the TGS collision system. The most comprehensive books on the subject are Geometric Tools for Computer Graphics (GTCG) and Real-Time Collision Detection (RTCD); the former is all-encompassing, the latter more approachable and focused.

컴퓨터 그래픽 분야에서 광범위하게 사용되는 핵심적인 알고리즘과 그를 구현하는 코드가 공개된 사이트.
Graphics Gems 시리즈 책에 실려있는 모든 코드가 고스란히 정리되고 공개되어 있다.
해석프로그램인 SolarView에서 사용한 알고리즘 중 일부는 여기에서 제공한 것을 번역 또는 변환해서 사용하였다.

주소 : http://tog.acm.org/GraphicsGems/
내용 :
2D Geometry
2D Rendering
3D Geometry
3D Rendering
C Utilities
Curves and Surfaces
Frame Buffer Techniques
Image Processing
Matrix Techniques
Modeling and Transformations
Numerical and Programming Techniques
Radiosity
Ray Tracing

이 책은 알고리즘, 프로그램, 그래픽 프로그래머들에 필요한 수학적인 기술들을 담고 있다. 즉, 그래픽 프로그래머들이 프로그램을 작성할 때 도움을
주고자 만들어졌다. 이 책에 있는 기사들은 연구 논문이 아니며, 저널에 실린 것들과 컨퍼런스에서 나온 결과를 담고 있다. 수록된 내용들과
소스코드는 현재까지 모든 게임과 그래픽 전 분야에 걸쳐서 핵심적으로 사용되고 있는 것들이다. (교보문고 설명문 인용)

유즈넷 Comp.Graphics.Algorithms에서 자주묻는질문(FAQ)를 정리해놓은 사이트

Table of
Contents

0. General Information

0.01:
Charter of comp.graphics.algorithms
0.02:
Are the postings to comp.graphics.algorithms archived?
0.03:
How can I get this FAQ?
0.04:
What are some must-have books on graphics algorithms?
0.05:
Are there any online references?
0.06:
Are there other graphics related FAQs?
0.07:
Where is all the source?

1. 2D Computations:
Points, Segments, Circles, Etc.

1.01:
How do I rotate a 2D point?
1.02:
How do I find the distance from a point to a line?
1.03:
How do I find intersections of 2 2D line segments?
1.04:
How do I generate a circle through three points?
1.05:
How can the smallest circle enclosing a set of points be
found?
1.06:
Where can I find graph layout algorithms?

2. 2D Polygon
Computations

2.01:
How do I find the area of a polygon?
2.02:
How can the centroid of a polygon be computed?
2.03:
How do I find if a point lies within a polygon?
2.04:
How do I find the intersection of two convex polygons?
2.05:
How do I do a hidden surface test (backface culling) with
2d points?
2.06:
How do I find a single point inside a simple polygon?
2.07:
How do I find the orientation of a simple polygon?

3. 2D Image/Pixel
Computations

3.01:
How do I rotate a bitmap?
3.02:
How do I display a 24 bit image in 8 bits?
3.03:
How do I fill the area of an arbitrary shape?
3.04:
How do I find the ‘edges’ in a bitmap?
3.05:
How do I enlarge/sharpen/fuzz a bitmap?
3.06:
How do I map a texture on to a shape?
3.07:
How do I detect a ‘corner’ in a collection of points?
3.08:
Where do I get source to display (raster font format)?
3.09:
What is morphing/how is it done?
3.10:
How do I quickly draw a filled triangle?
3.11:
D Noise functions and turbulence in Solid texturing.
3.12:
How do I generate realistic sythetic textures?
3.13:
How do I convert between color models (RGB, HLS, CMYK,
CIE etc)?
3.14:
How is “GIF” pronounced?

4. Curve Computations

4.01:
How do I generate a bezier curve that is parallel to
another bezier?
4.02:
How do I split a bezier at a specific value for t?
4.03:
How do I find a t value at a specific point on a bezier?
4.04:
How do I fit a bezier curve to a circle?

5. 3D computations

5.01:
How do I rotate a 3D point?
5.02:
What is ARCBALL and where is the source?
5.03:
How do I clip a polygon against a rectangle?
5.04:
How do I clip a polygon against another polygon?
5.05:
How do I find the intersection of a line and a plane?
5.06:
How do I determine the intersection between a ray and a
polygon?
5.07:
How do I determine the intersection between a ray and a
sphere?
5.08:
How do I find the intersection of a ray and a bezier
surface?
5.09:
How do I ray trace caustics?
5.10:
What is the marching cubes algorithm?
5.11:
What is the status of the patent on the “marching
cubes” algorithm?
5.12:
How do I do a hidden surface test (backface culling) with
3d points?
5.13:
Where can I find algorithms for 3D collision detection?
5.14:
How do I perform basic viewing in 3d?
5.15:
How do I optimize a 3D polygon mesh?
5.16:
How can I perform volume rendering?
5.17:
Where can I get the spline description of the famous
teapot etc.?
5.18:
How can the distance between two lines in space be
computed?
5.19:
How can I compute the volume of a polyhedron?
5.20:
How can I decompose a polyhedron into convex pieces?
5.21:
How can the circumsphere of a tetrahedron be computed?
5.22:
How do I determine if two triangles in 3D intersect?

6. Geometric Structures
and Mathematics

6.01:
Where can I get source for Voronoi/Delaunay
triangulation?
6.02:
Where do I get source for convex hull?
6.03:
Where do I get source for halfspace intersection?
6.04:
What are barycentric coordinates?
6.05:
How do I generate a random point inside a triangle?
6.06:
How do I evenly distribute N points on (tesselate) a
sphere?
6.07:
What are coordinates for the vertices of an icosohedron?
6.08:
How do I generate random points on the surface of a
sphere?
6.09:
What are Plücker coordinates?

7. Contributors

7.01:
How can you contribute to this FAQ?
7.02:
Contributors. Who made this all possible.