# Math for Computer Graphics and Computer Vision

(Difference between revisions)
 Revision as of 10:27, 1 September 2009 (edit)← Previous diff Revision as of 16:43, 21 June 2011 (edit) (undo)Next diff → Line 7: Line 7: The following is a list of mathematical topics used in computer graphics. The original list was provided by Drexel professor David Breen. The following is a list of mathematical topics used in computer graphics. The original list was provided by Drexel professor David Breen. + :* 2D, 3D, 4D real spaces; affine subspaces; homogeneous coordinates :* [[Vector |Vectors]] and [[Matrix |Matrices]] :* [[Vector |Vectors]] and [[Matrix |Matrices]] + :* Graphics primitives + ::* 2D primitives developed from triangles: fans, strips + ::* Convexity and convex sums + ::* 3D models based on 2D faces + ::* ''Do we save machine representations for the CG course?'' + :* Transformations :* Transformations ::*[[Transformation Matrix]] ::*[[Transformation Matrix]] + :::* Primitive geometric transformations + :::* Creating general transformations via sequences of primitives + :::* Inverse transformations via primitives + :::* ''Do we include transformation stacks?'' ::*[[Change Of Coordinate Transformations]] ::*[[Change Of Coordinate Transformations]] + :::* This might well be phrased in terms of the viewing transformation + :* [[Quaternion|Quaternions]] :* [[Quaternion|Quaternions]] + :* Hierarchical coordinate systems :* Hierarchical coordinate systems + :* Geometry :* Geometry - ::* Curves (Catmull-Rom, Bezier, B-spline) - ::* Bezier patches - ::* Subdivision surfaces ::* Implicit geometry - lines, circles, ellipses ::* Implicit geometry - lines, circles, ellipses ::* [[Implicit Surfaces]] - quadrics, superquadrics ::* [[Implicit Surfaces]] - quadrics, superquadrics ::* [[Implicit Equations]] ::* [[Implicit Equations]] ::* [[Parametric Equations|Parametric geometry]] - lines, circles, ellipses ::* [[Parametric Equations|Parametric geometry]] - lines, circles, ellipses + ::* Curves (Catmull-Rom, Bezier, B-spline) ::* Parametric surfaces - quadrics, superquadrics ::* Parametric surfaces - quadrics, superquadrics + ::* Bezier patches + ::* Subdivision surfaces ::*[[Procedural Image]] ::*[[Procedural Image]] :* Surface normals :* Surface normals + ::* Techniques of computing them from analytic and non-analytic cases :* Silhouette edges :* Silhouette edges :* Procedural texture maps :* Procedural texture maps + ::* Noise :* Ray-object intersection :* Ray-object intersection + ::* ''Bounding spheres and boxes?'' :* [[Planar Projection|Perspective and parallel planar projections]] :* [[Planar Projection|Perspective and parallel planar projections]] :* Non-planar projections :* Non-planar projections

## Revision as of 16:43, 21 June 2011

Not surprisingly, the mathematics used in computer graphics was touched upon by the students at Drexel and Swarthmore during the summer of '09. Some of the Helper Pages, in particular are needed topics for some of the image pages, and for computer graphics.

As students turned their creative talents on these topics we decided to open this repository of software devoted to understanding them. Our hope is that it will develop into a useful resource for students and faculty in both disciplines. Please contribute your good material!

The following is a list of mathematical topics used in computer graphics. The original list was provided by Drexel professor David Breen.

• 2D, 3D, 4D real spaces; affine subspaces; homogeneous coordinates
• Vectors and Matrices
• Graphics primitives
• 2D primitives developed from triangles: fans, strips
• Convexity and convex sums
• 3D models based on 2D faces
• Do we save machine representations for the CG course?
• Transformations
• Primitive geometric transformations
• Creating general transformations via sequences of primitives
• Inverse transformations via primitives
• Do we include transformation stacks?
• This might well be phrased in terms of the viewing transformation
• Hierarchical coordinate systems
• Geometry
• Surface normals
• Techniques of computing them from analytic and non-analytic cases
• Silhouette edges
• Procedural texture maps
• Noise
• Ray-object intersection
• Bounding spheres and boxes?

More examples may be found in the lecture slides of CS 430.