官术网_书友最值得收藏!

Matrices

In computer graphics, matrices are used to calculate object transforms like translation which is movement, scaling in X,Y and Z axis, and rotation around the X,Y and Z axis. We will also be changing the position of objects from one coordinate system to the other, which are called space transforms. We will see how matrices work and how they help in simplifying the mathematics.

Matrices are represented as having rows and columns. A matrix with m number of rows and n number of columns is said to be a matrix of size m × n. Each element of a matrix is represented as indices ij where i specifies the row number and j represents the column number.

So, a matrix M of size 3 × 2 is represented as as follows:

Here, matrix M has three rows and two columns and each element is represented as m11, m12 and so on until m32, which is the size of the matrix.

In 3D graphics programming, we will be mostly dealing with a 4×4 matrix. So, let us look at another matrix of size 4x4.

Matrix A with numbers in it is:

Here, the element A11 = 3, A32 = 1 and A44 = 1 and the dimension of the matrix is 4×4.

We can also have a single-dimension matrix like vector B as follows which is called the row vector or a column vector as shown as follows ad vector C:

  • Two matrices are equal if the number of rows and columns are the same and if the corresponding elements are of the same value.
  • Two matrices can be added if they have the same number of rows and columns. We add each element of the corresponding location on both matrices to get a third matrix of the same dimension as the added matrices.
主站蜘蛛池模板: 淮南市| 菏泽市| 偃师市| 牙克石市| 安丘市| 沧州市| 浪卡子县| 北流市| 舟山市| 乡宁县| 泸定县| 冀州市| 四子王旗| 濮阳市| 同德县| 栖霞市| 湖北省| 金乡县| 安义县| 丰顺县| 富民县| 乐山市| 乃东县| 潼关县| 阿克苏市| 托里县| 英山县| 巴彦淖尔市| 峡江县| 赣榆县| 昭觉县| 汶川县| 武安市| 宁乡县| 门头沟区| 古浪县| 三原县| 阿图什市| 余江县| 罗山县| 化德县|