com.funzio.pure2D.geom

Class Matrix

java.lang.Object

com.funzio.pure2D.geom.Matrix

public class Matrix
extends java.lang.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:

java.lang.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:

java.lang.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