Presentation is loading. Please wait.

Presentation is loading. Please wait.

Maths for Computer Graphics

Similar presentations

Presentation on theme: "Maths for Computer Graphics"— Presentation transcript:

1 Maths for Computer Graphics 2011-2012
Matrices Maths for Computer Graphics

2 Matrix Matrix an array of numbers arranged into m rows and n columns:
i = 1, …, m Columns, j = 1, …, n

3 Row and Column Matrices (vectors)‏
row matrix (or row vector) is a matrix with one row column vector is a matrix with only one column

4 Square Matrix When the row and column dimensions of a matrix are equal (m = n) then the matrix is called square matrix

5 Matrix Equality Two (m x n) matrices A and B are equal if and only if each of their elements are equal. That is A = B if and only if aij = bij for all i = 1,...,m; j = 1,...,n

6 Matrix Addition 2x2 Matrix addition

7 Matrix Addition

8 Examples - Matrix Addition
The following matrix addition is not defined

9 Scalar – Matrix Multiplication
Multiplication of a matrix A by a scalar is defined as follows Example

10 Matrix – Matrix Multiplication
The product of two matrices A and B is defined only if the number of columns of A is equal to the number of rows of B. If A is (m x p) and B is (p x n), the product is an (m x n) matrix C

11 Matrix – Matrix Multiplication

12 Matrix – Matrix Multiplication

13 Example - Matrix Multiplication

14 Example - Matrix Multiplication

15 Example - Matrix Multiplication

16 Identity Matrix Identity Matrix
The identity matrix has the property that if A is a square matrix, then

Download ppt "Maths for Computer Graphics"

Similar presentations

Ads by Google