# IT. Expert System.

android.opengl

## Class Matrix

• ```public class Matrix
extends Object```
Matrix math utilities. These methods operate on OpenGL ES format matrices and vectors stored in float arrays. Matrices are 4 x 4 column-vector matrices stored in column-major order:
```  m[offset +  0] m[offset +  4] m[offset +  8] m[offset + 12]
m[offset +  1] m[offset +  5] m[offset +  9] m[offset + 13]
m[offset +  2] m[offset +  6] m[offset + 10] m[offset + 14]
m[offset +  3] m[offset +  7] m[offset + 11] m[offset + 15]
```
Vectors are 4 row x 1 column column-vectors stored in order:
``` v[offset + 0]
v[offset + 1]
v[offset + 2]
v[offset + 3]
```
• ### Constructor Summary

Constructors
Constructor and Description
`Matrix()`
• ### Method Summary

Methods
Modifier and Type Method and Description
`static void` ```frustumM(float[] m, int offset, float left, float right, float bottom, float top, float near, float far)```
Define a projection matrix in terms of six clip planes
`static boolean` ```invertM(float[] mInv, int mInvOffset, float[] m, int mOffset)```
Inverts a 4 x 4 matrix.
`static float` ```length(float x, float y, float z)```
Computes the length of a vector
`static void` ```multiplyMM(float[] result, int resultOffset, float[] lhs, int lhsOffset, float[] rhs, int rhsOffset)```
Multiply two 4x4 matrices together and store the result in a third 4x4 matrix.
`static void` ```multiplyMV(float[] resultVec, int resultVecOffset, float[] lhsMat, int lhsMatOffset, float[] rhsVec, int rhsVecOffset)```
Multiply a 4 element vector by a 4x4 matrix and store the result in a 4 element column vector.
`static void` ```orthoM(float[] m, int mOffset, float left, float right, float bottom, float top, float near, float far)```
Computes an orthographic projection matrix.
`static void` ```perspectiveM(float[] m, int offset, float fovy, float aspect, float zNear, float zFar)```
Define a projection matrix in terms of a field of view angle, an aspect ratio, and z clip planes
`static void` ```rotateM(float[] rm, int rmOffset, float[] m, int mOffset, float a, float x, float y, float z)```
Rotates matrix m by angle a (in degrees) around the axis (x, y, z)
`static void` ```rotateM(float[] m, int mOffset, float a, float x, float y, float z)```
Rotates matrix m in place by angle a (in degrees) around the axis (x, y, z)
`static void` ```scaleM(float[] sm, int smOffset, float[] m, int mOffset, float x, float y, float z)```
Scales matrix m by x, y, and z, putting the result in sm
`static void` ```scaleM(float[] m, int mOffset, float x, float y, float z)```
Scales matrix m in place by sx, sy, and sz
`static void` ```setIdentityM(float[] sm, int smOffset)```
Sets matrix m to the identity matrix.
`static void` ```setLookAtM(float[] rm, int rmOffset, float eyeX, float eyeY, float eyeZ, float centerX, float centerY, float centerZ, float upX, float upY, float upZ)```
Define a viewing transformation in terms of an eye point, a center of view, and an up vector.
`static void` ```setRotateEulerM(float[] rm, int rmOffset, float x, float y, float z)```
Converts Euler angles to a rotation matrix
`static void` ```setRotateM(float[] rm, int rmOffset, float a, float x, float y, float z)```
Rotates matrix m by angle a (in degrees) around the axis (x, y, z)
`static void` ```translateM(float[] tm, int tmOffset, float[] m, int mOffset, float x, float y, float z)```
Translates matrix m by x, y, and z, putting the result in tm
`static void` ```translateM(float[] m, int mOffset, float x, float y, float z)```
Translates matrix m by x, y, and z in place.
`static void` ```transposeM(float[] mTrans, int mTransOffset, float[] m, int mOffset)```
Transposes a 4 x 4 matrix.
• ### Methods inherited from class java.lang.Object

`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### Constructor Detail

• #### Matrix

`public Matrix()`
• ### Method Detail

• #### multiplyMM

```public static void multiplyMM(float[] result,
int resultOffset,
float[] lhs,
int lhsOffset,
float[] rhs,
int rhsOffset)```
Multiply two 4x4 matrices together and store the result in a third 4x4 matrix. In matrix notation: result = lhs x rhs. Due to the way matrix multiplication works, the result matrix will have the same effect as first multiplying by the rhs matrix, then multiplying by the lhs matrix. This is the opposite of what you might expect. The same float array may be passed for result, lhs, and/or rhs. However, the result element values are undefined if the result elements overlap either the lhs or rhs elements.
Parameters:
`result` - The float array that holds the result.
`resultOffset` - The offset into the result array where the result is stored.
`lhs` - The float array that holds the left-hand-side matrix.
`lhsOffset` - The offset into the lhs array where the lhs is stored
`rhs` - The float array that holds the right-hand-side matrix.
`rhsOffset` - The offset into the rhs array where the rhs is stored.
Throws:
`IllegalArgumentException` - if result, lhs, or rhs are null, or if resultOffset + 16 > result.length or lhsOffset + 16 > lhs.length or rhsOffset + 16 > rhs.length.
• #### multiplyMV

```public static void multiplyMV(float[] resultVec,
int resultVecOffset,
float[] lhsMat,
int lhsMatOffset,
float[] rhsVec,
int rhsVecOffset)```
Multiply a 4 element vector by a 4x4 matrix and store the result in a 4 element column vector. In matrix notation: result = lhs x rhs The same float array may be passed for resultVec, lhsMat, and/or rhsVec. However, the resultVec element values are undefined if the resultVec elements overlap either the lhsMat or rhsVec elements.
Parameters:
`resultVec` - The float array that holds the result vector.
`resultVecOffset` - The offset into the result array where the result vector is stored.
`lhsMat` - The float array that holds the left-hand-side matrix.
`lhsMatOffset` - The offset into the lhs array where the lhs is stored
`rhsVec` - The float array that holds the right-hand-side vector.
`rhsVecOffset` - The offset into the rhs vector where the rhs vector is stored.
Throws:
`IllegalArgumentException` - if resultVec, lhsMat, or rhsVec are null, or if resultVecOffset + 4 > resultVec.length or lhsMatOffset + 16 > lhsMat.length or rhsVecOffset + 4 > rhsVec.length.
• #### transposeM

```public static void transposeM(float[] mTrans,
int mTransOffset,
float[] m,
int mOffset)```
Transposes a 4 x 4 matrix.
Parameters:
`mTrans` - the array that holds the output inverted matrix
`mTransOffset` - an offset into mInv where the inverted matrix is stored.
`m` - the input array
`mOffset` - an offset into m where the matrix is stored.
• #### invertM

```public static boolean invertM(float[] mInv,
int mInvOffset,
float[] m,
int mOffset)```
Inverts a 4 x 4 matrix.
Parameters:
`mInv` - the array that holds the output inverted matrix
`mInvOffset` - an offset into mInv where the inverted matrix is stored.
`m` - the input array
`mOffset` - an offset into m where the matrix is stored.
Returns:
true if the matrix could be inverted, false if it could not.
• #### orthoM

```public static void orthoM(float[] m,
int mOffset,
float left,
float right,
float bottom,
float top,
float near,
float far)```
Computes an orthographic projection matrix.
Parameters:
`m` - returns the result
`mOffset` -
`left` -
`right` -
`bottom` -
`top` -
`near` -
`far` -
• #### frustumM

```public static void frustumM(float[] m,
int offset,
float left,
float right,
float bottom,
float top,
float near,
float far)```
Define a projection matrix in terms of six clip planes
Parameters:
`m` - the float array that holds the perspective matrix
`offset` - the offset into float array m where the perspective matrix data is written
`left` -
`right` -
`bottom` -
`top` -
`near` -
`far` -
• #### perspectiveM

```public static void perspectiveM(float[] m,
int offset,
float fovy,
float aspect,
float zNear,
float zFar)```
Define a projection matrix in terms of a field of view angle, an aspect ratio, and z clip planes
Parameters:
`m` - the float array that holds the perspective matrix
`offset` - the offset into float array m where the perspective matrix data is written
`fovy` - field of view in y direction, in degrees
`aspect` - width to height aspect ratio of the viewport
`zNear` -
`zFar` -
• #### length

```public static float length(float x,
float y,
float z)```
Computes the length of a vector
Parameters:
`x` - x coordinate of a vector
`y` - y coordinate of a vector
`z` - z coordinate of a vector
Returns:
the length of a vector
• #### setIdentityM

```public static void setIdentityM(float[] sm,
int smOffset)```
Sets matrix m to the identity matrix.
Parameters:
`sm` - returns the result
`smOffset` - index into sm where the result matrix starts
• #### scaleM

```public static void scaleM(float[] sm,
int smOffset,
float[] m,
int mOffset,
float x,
float y,
float z)```
Scales matrix m by x, y, and z, putting the result in sm
Parameters:
`sm` - returns the result
`smOffset` - index into sm where the result matrix starts
`m` - source matrix
`mOffset` - index into m where the source matrix starts
`x` - scale factor x
`y` - scale factor y
`z` - scale factor z
• #### scaleM

```public static void scaleM(float[] m,
int mOffset,
float x,
float y,
float z)```
Scales matrix m in place by sx, sy, and sz
Parameters:
`m` - matrix to scale
`mOffset` - index into m where the matrix starts
`x` - scale factor x
`y` - scale factor y
`z` - scale factor z
• #### translateM

```public static void translateM(float[] tm,
int tmOffset,
float[] m,
int mOffset,
float x,
float y,
float z)```
Translates matrix m by x, y, and z, putting the result in tm
Parameters:
`tm` - returns the result
`tmOffset` - index into sm where the result matrix starts
`m` - source matrix
`mOffset` - index into m where the source matrix starts
`x` - translation factor x
`y` - translation factor y
`z` - translation factor z
• #### translateM

```public static void translateM(float[] m,
int mOffset,
float x,
float y,
float z)```
Translates matrix m by x, y, and z in place.
Parameters:
`m` - matrix
`mOffset` - index into m where the matrix starts
`x` - translation factor x
`y` - translation factor y
`z` - translation factor z
• #### rotateM

```public static void rotateM(float[] rm,
int rmOffset,
float[] m,
int mOffset,
float a,
float x,
float y,
float z)```
Rotates matrix m by angle a (in degrees) around the axis (x, y, z)
Parameters:
`rm` - returns the result
`rmOffset` - index into rm where the result matrix starts
`m` - source matrix
`mOffset` - index into m where the source matrix starts
`a` - angle to rotate in degrees
`x` - scale factor x
`y` - scale factor y
`z` - scale factor z
• #### rotateM

```public static void rotateM(float[] m,
int mOffset,
float a,
float x,
float y,
float z)```
Rotates matrix m in place by angle a (in degrees) around the axis (x, y, z)
Parameters:
`m` - source matrix
`mOffset` - index into m where the matrix starts
`a` - angle to rotate in degrees
`x` - scale factor x
`y` - scale factor y
`z` - scale factor z
• #### setRotateM

```public static void setRotateM(float[] rm,
int rmOffset,
float a,
float x,
float y,
float z)```
Rotates matrix m by angle a (in degrees) around the axis (x, y, z)
Parameters:
`rm` - returns the result
`rmOffset` - index into rm where the result matrix starts
`a` - angle to rotate in degrees
`x` - scale factor x
`y` - scale factor y
`z` - scale factor z
• #### setRotateEulerM

```public static void setRotateEulerM(float[] rm,
int rmOffset,
float x,
float y,
float z)```
Converts Euler angles to a rotation matrix
Parameters:
`rm` - returns the result
`rmOffset` - index into rm where the result matrix starts
`x` - angle of rotation, in degrees
`y` - angle of rotation, in degrees
`z` - angle of rotation, in degrees
• #### setLookAtM

```public static void setLookAtM(float[] rm,
int rmOffset,
float eyeX,
float eyeY,
float eyeZ,
float centerX,
float centerY,
float centerZ,
float upX,
float upY,
float upZ)```
Define a viewing transformation in terms of an eye point, a center of view, and an up vector.
Parameters:
`rm` - returns the result
`rmOffset` - index into rm where the result matrix starts
`eyeX` - eye point X
`eyeY` - eye point Y
`eyeZ` - eye point Z
`centerX` - center of view X
`centerY` - center of view Y
`centerZ` - center of view Z
`upX` - up vector X
`upY` - up vector Y
`upZ` - up vector Z

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