# linear algebra techniques used in computer graphics

Why is linear algebra important for computer graphics? How are linear algebra techniques used in computer graphics?

Please review the following link,Mathematics for Computer Graphics, Retrieved February 29, 2008, from http://www.cc.gatech.edu/~turk/math_gr.htmlVectors and Matrices, Retrieved February 29, 2008, from http://www.ncrg.aston.ac.uk/~cornfosd/graphics/pdf/vector_eg.pdf3D Geometry Primer, Retrieved February 29, 2008, from http://flipcode.com/geometry/index.shtmlVector Math for 3D Computer Graphics, Retrieved February 29, 2008, from http://chortle.ccsu.edu/VectorLessons/vectorIndex.html

#### Solution Preview

Full Problem Description: Why is linear algebra important for computer graphics?How

are linear algebra techniques used in computer graphics?

Please review the following link,Mathematics for Computer Graphics, Retrieved February

29, 2008, from http://www.cc.gatech.edu/~turk/math_gr.htmlVectors and Matrices,

Retrieved February 29, 2008, from

http://www.ncrg.aston.ac.uk/~cornfosd/graphics/pdf/vector_eg.pdf3D Geometry Primer,

Retrieved February 29, 2008, from http://flipcode.com/geometry/index.shtmlVector Math

for 3D Computer Graphics,

Retrieved February 29, 2008, from

http://chortle.ccsu.edu/VectorLessons/vectorIndex.html

Solution Description:

Notes from readings:

http://www.cc.gatech.edu/~turk/math_gr.html

1)High-school level algebra and trigonometry

2)The ideas of linear algebra are used throughout computer graphics. In fact, any area

that concerns itself with numerical representations of geometry often will collect

together numbers such as x,y,z positions into mathematical objects called vectors.

Vectors and a related mathematical object called a matrix are used all the time in

graphics. The language of vectors and matrices is an elegant way to describe (among

other things) the way in which an object may be rotated, shifted (translated), or made

larger or smaller (scaled).

3) Differential Geometry. This area of mathematics studies equations that govern the

geometry of smooth curves and surfaces. If you are trying to figure out what direction

is perpendicular to (points directly away from) a smooth surface (the "normal vector")

then you are using differential geometry.

4) Numerical Methods using manipulate numbers in the computer we use ...

#### Solution Summary

The goal of this solution is to assist the student in answering some basic questions on computer graphics and how linear algebra is used. Several articles are given in the problem statement as part of the review material.