public final class FloatUtil extends Object
Implementation assumes linear matrix layout in column-major order matching OpenGL's implementation, illustration:
Row-Major Column-Major (OpenGL):
| 0 1 2 3 | | 0 4 8 12 |
| | | |
| 4 5 6 7 | | 1 5 9 13 |
M = | | M = | |
| 8 9 10 11 | | 2 6 10 14 |
| | | |
| 12 13 14 15 | | 3 7 11 15 |
C R C R
m[0*4+3] = tx; m[0+4*3] = tx;
m[1*4+3] = ty; m[1+4*3] = ty;
m[2*4+3] = tz; m[2+4*3] = tz;
Implementation utilizes unrolling of small vertices and matrices wherever possible while trying to access memory in a linear fashion for performance reasons, see:
| Modifier and Type | Field and Description |
|---|---|
static boolean |
DEBUG |
static float |
E |
static float |
EPSILON
Epsilon for floating point 1.1920928955078125E-7f, as once computed via
getMachineEpsilon() on an AMD-64 CPU. |
static float |
HALF_PI
The value PI/2, i.e.
|
static float |
INV_DEVIANCE
Inversion Epsilon, used with equals method to determine if two inverted matrices are close enough to be considered equal.
|
static float |
PI
The value PI, i.e.
|
static float |
QUARTER_PI
The value PI/4, i.e.
|
static float |
SQUARED_PI
The value PI^2.
|
static float |
TWO_PI
The value 2PI, i.e.
|
| Constructor and Description |
|---|
FloatUtil() |
| Modifier and Type | Method and Description |
|---|---|
static float |
abs(float a) |
static float |
acos(float a) |
static float |
asin(float a) |
static float |
atan(float a) |
static float |
atan2(float y,
float x) |
static int |
compare(float a,
float b)
Return true if both values are equal w/o regarding an epsilon.
|
static int |
compare(float a,
float b,
float epsilon)
Return true if both values are equal, i.e.
|
static float[] |
copyMatrixColumn(float[] m_in,
int m_in_off,
int column,
float[] v_out,
int v_out_off)
Copy the named column of the given column-major matrix to v_out.
|
static float[] |
copyMatrixRow(float[] m_in,
int m_in_off,
int row,
float[] v_out,
int v_out_off)
Copy the named row of the given column-major matrix to v_out.
|
static float |
cos(float a) |
static float |
getMachineEpsilon()
Return computed machine Epsilon value.
|
static float |
getOrthoWinZ(float orthoZ,
float zNear,
float zFar)
Returns orthogonal distance
(1f/zNear-1f/orthoDist)/(1f/zNear-1f/zFar);
|
static float |
getZBufferEpsilon(int zBits,
float z,
float zNear)
Returns resolution of Z buffer of given parameter,
see Love Your Z-Buffer.
|
static int |
getZBufferValue(int zBits,
float z,
float zNear,
float zFar)
Returns Z buffer value of given parameter,
see Love Your Z-Buffer.
|
static float[] |
invertMatrix(float[] msrc,
float[] mres)
Invert the given matrix.
|
static float[] |
invertMatrix(float[] msrc,
int msrc_offset,
float[] mres,
int mres_offset)
Invert the given matrix.
|
static boolean |
isEqual(float a,
float b)
Return true if both values are equal w/o regarding an epsilon.
|
static boolean |
isEqual(float a,
float b,
float epsilon)
Return true if both values are equal, i.e.
|
static boolean |
isZero(float a,
float epsilon)
Return true if value is zero, i.e.
|
static float[] |
makeFrustum(float[] m,
int m_offset,
boolean initM,
float left,
float right,
float bottom,
float top,
float zNear,
float zFar)
Make given matrix the frustum matrix based on given parameters.
|
static float[] |
makeIdentity(float[] m)
Make matrix an identity matrix
|
static float[] |
makeIdentity(float[] m,
int m_offset)
Make matrix an identity matrix
|
static float[] |
makeLookAt(float[] m,
int m_offset,
float[] eye,
int eye_offset,
float[] center,
int center_offset,
float[] up,
int up_offset,
float[] mat4Tmp)
Make given matrix the look-at matrix based on given parameters.
|
static float[] |
makeOrtho(float[] m,
int m_offset,
boolean initM,
float left,
float right,
float bottom,
float top,
float zNear,
float zFar)
Make given matrix the orthogonal matrix based on given parameters.
|
static float[] |
makePerspective(float[] m,
int m_off,
boolean initM,
float fovy_rad,
float aspect,
float zNear,
float zFar)
Make given matrix the perspective
frustum
matrix based on given parameters. |
static float[] |
makePerspective(float[] m,
int m_offset,
boolean initM,
FovHVHalves fovhv,
float zNear,
float zFar)
Make given matrix the perspective
frustum
matrix based on given parameters. |
static float[] |
makePick(float[] m,
int m_offset,
float x,
float y,
float deltaX,
float deltaY,
int[] viewport,
int viewport_offset,
float[] mat4Tmp)
Make given matrix the pick matrix based on given parameters.
|
static float[] |
makeRotationAxis(float[] m,
int m_offset,
float angrad,
float x,
float y,
float z,
float[] tmpVec3f)
Make a rotation matrix from the given axis and angle in radians.
|
static float[] |
makeRotationEuler(float[] m,
int m_offset,
float bankX,
float headingY,
float attitudeZ)
Make a concatenated rotation matrix in column-major order from the given Euler rotation angles in radians.
|
static float[] |
makeScale(float[] m,
boolean initM,
float sx,
float sy,
float sz)
Make a scale matrix in column-major order from the given axis factors
|
static float[] |
makeScale(float[] m,
int m_offset,
boolean initM,
float sx,
float sy,
float sz)
Make a scale matrix in column-major order from the given axis factors
|
static float[] |
makeTranslation(float[] m,
boolean initM,
float tx,
float ty,
float tz)
Make a translation matrix in column-major order from the given axis deltas
|
static float[] |
makeTranslation(float[] m,
int m_offset,
boolean initM,
float tx,
float ty,
float tz)
Make a translation matrix in column-major order from the given axis deltas
|
static boolean |
mapObjToWinCoords(float objx,
float objy,
float objz,
float[] mat4PMv,
int[] viewport,
int viewport_offset,
float[] win_pos,
int win_pos_offset,
float[] vec4Tmp1,
float[] vec4Tmp2)
Map object coordinates to window coordinates.
|
static boolean |
mapObjToWinCoords(float objx,
float objy,
float objz,
float[] modelMatrix,
int modelMatrix_offset,
float[] projMatrix,
int projMatrix_offset,
int[] viewport,
int viewport_offset,
float[] win_pos,
int win_pos_offset,
float[] vec4Tmp1,
float[] vec4Tmp2)
Map object coordinates to window coordinates.
|
static boolean |
mapWinToObjCoords(float winx,
float winy,
float winz,
float[] mat4PMvI,
int[] viewport,
int viewport_offset,
float[] obj_pos,
int obj_pos_offset,
float[] vec4Tmp1,
float[] vec4Tmp2)
Map window coordinates to object coordinates.
|
static boolean |
mapWinToObjCoords(float winx,
float winy,
float winz,
float[] modelMatrix,
int modelMatrix_offset,
float[] projMatrix,
int projMatrix_offset,
int[] viewport,
int viewport_offset,
float[] obj_pos,
int obj_pos_offset,
float[] mat4Tmp1,
float[] mat4Tmp2)
Map window coordinates to object coordinates.
|
static boolean |
mapWinToObjCoords(float winx,
float winy,
float winz1,
float winz2,
float[] mat4PMvI,
int[] viewport,
int viewport_offset,
float[] obj1_pos,
int obj1_pos_offset,
float[] obj2_pos,
int obj2_pos_offset,
float[] vec4Tmp1,
float[] vec4Tmp2)
Map two window coordinates to two object coordinates,
distinguished by their z component.
|
static boolean |
mapWinToObjCoords(float winx,
float winy,
float winz,
float clipw,
float[] modelMatrix,
int modelMatrix_offset,
float[] projMatrix,
int projMatrix_offset,
int[] viewport,
int viewport_offset,
float near,
float far,
float[] obj_pos,
int obj_pos_offset,
float[] mat4Tmp1,
float[] mat4Tmp2)
Map window coordinates to object coordinates.
|
static boolean |
mapWinToRay(float winx,
float winy,
float winz0,
float winz1,
float[] modelMatrix,
int modelMatrix_offset,
float[] projMatrix,
int projMatrix_offset,
int[] viewport,
int viewport_offset,
Ray ray,
float[] mat4Tmp1,
float[] mat4Tmp2,
float[] vec4Tmp2)
Map two window coordinates w/ shared X/Y and distinctive Z
to a
Ray. |
static float |
matrixDeterminant(float[] m)
Returns the determinant of the given matrix
|
static float |
matrixDeterminant(float[] m,
int m_offset)
Returns the determinant of the given matrix
|
static StringBuilder |
matrixRowToString(StringBuilder sb,
String f,
float[] a,
int aOffset,
int rows,
int columns,
boolean rowMajorOrder,
int row) |
static StringBuilder |
matrixRowToString(StringBuilder sb,
String f,
FloatBuffer a,
int aOffset,
int rows,
int columns,
boolean rowMajorOrder,
int row)
Deprecated.
use on of the float[] variants
|
static StringBuilder |
matrixToString(StringBuilder sb,
String rowPrefix,
String f,
float[] a,
int aOffset,
float[] b,
int bOffset,
int rows,
int columns,
boolean rowMajorOrder) |
static StringBuilder |
matrixToString(StringBuilder sb,
String rowPrefix,
String f,
float[] a,
int aOffset,
int rows,
int columns,
boolean rowMajorOrder) |
static StringBuilder |
matrixToString(StringBuilder sb,
String rowPrefix,
String f,
FloatBuffer a,
int aOffset,
FloatBuffer b,
int bOffset,
int rows,
int columns,
boolean rowMajorOrder)
Deprecated.
use on of the float[] variants
|
static StringBuilder |
matrixToString(StringBuilder sb,
String rowPrefix,
String f,
FloatBuffer a,
int aOffset,
int rows,
int columns,
boolean rowMajorOrder)
Deprecated.
use on of the float[] variants
|
static float[] |
multMatrix(float[] a,
float[] b)
Multiply matrix: [a] = [a] x [b]
|
static float[] |
multMatrix(float[] a,
float[] b,
float[] d)
Multiply matrix: [d] = [a] x [b]
|
static float[] |
multMatrix(float[] a,
int a_off,
float[] b,
int b_off)
Multiply matrix: [a] = [a] x [b]
|
static float[] |
multMatrix(float[] a,
int a_off,
float[] b,
int b_off,
float[] d,
int d_off)
Multiply matrix: [d] = [a] x [b]
|
static void |
multMatrix(FloatBuffer a,
FloatBuffer b)
Deprecated.
use on of the float[] variants
|
static void |
multMatrix(FloatBuffer a,
FloatBuffer b,
float[] d)
Deprecated.
use on of the float[] variants
|
static float[] |
multMatrixVec(float[] m_in,
float[] v_in,
float[] v_out) |
static float[] |
multMatrixVec(float[] m_in,
int m_in_off,
float[] v_in,
int v_in_off,
float[] v_out,
int v_out_off) |
static void |
multMatrixVec(FloatBuffer m_in,
float[] v_in,
float[] v_out)
Deprecated.
use on of the float[] variants
|
static float |
pow(float a,
float b) |
static float |
sin(float a) |
static float |
sqrt(float a) |
static float |
tan(float a) |
static float[] |
transposeMatrix(float[] msrc,
float[] mres)
Transpose the given matrix.
|
static float[] |
transposeMatrix(float[] msrc,
int msrc_offset,
float[] mres,
int mres_offset)
Transpose the given matrix.
|
public static final boolean DEBUG
public static final float E
public static final float PI
public static final float TWO_PI
public static final float HALF_PI
public static final float QUARTER_PI
public static final float SQUARED_PI
public static final float EPSILON
getMachineEpsilon() on an AMD-64 CPU.
Definition of machine epsilon guarantees that:
1.0f + EPSILON != 1.0f
In other words: machEps is the maximum relative error of the chosen rounding procedure.
A number can be considered zero if it is in the range (or in the set):
MaybeZeroSet e ]-machEps .. machEps[ (exclusive)
While comparing floating point values, machEps allows to clip the relative error:
boolean isZero = afloat < EPSILON;
boolean isNotZero = afloat >= EPSILON;
boolean isEqual = abs(bfloat - afloat) < EPSILON;
boolean isNotEqual = abs(bfloat - afloat) >= EPSILON;
public static final float INV_DEVIANCE
Using 9.999999747378752E-6f, which is ~100 times EPSILON.
public static float[] makeIdentity(float[] m,
int m_offset)
m - 4x4 matrix in column-major order (also result)m_offset - offset in given array m, i.e. start of the 4x4 matrixpublic static float[] makeIdentity(float[] m)
m - 4x4 matrix in column-major order (also result)public static float[] makeTranslation(float[] m,
int m_offset,
boolean initM,
float tx,
float ty,
float tz)
Translation matrix (Column Order):
1 0 0 0
0 1 0 0
0 0 1 0
x y z 1
All matrix fields are only set if initM is true.
m - 4x4 matrix in column-major order (also result)m_offset - offset in given array m, i.e. start of the 4x4 matrixinitM - if true, given matrix will be initialized w/ identity matrix,
otherwise only the diagonal and last-row is set.
The latter can be utilized to share a once identity set matrix
for scaling
and translation,
while leaving the other fields untouched for performance reasons.public static float[] makeTranslation(float[] m,
boolean initM,
float tx,
float ty,
float tz)
Translation matrix (Column Order):
1 0 0 0
0 1 0 0
0 0 1 0
x y z 1
All matrix fields are only set if initM is true.
m - 4x4 matrix in column-major order (also result)initM - if true, given matrix will be initialized w/ identity matrix,
otherwise only the diagonal and last-row is set.
The latter can be utilized to share a once identity set matrix
for scaling
and translation,
while leaving the other fields untouched for performance reasons.public static float[] makeScale(float[] m,
int m_offset,
boolean initM,
float sx,
float sy,
float sz)
Scale matrix (Any Order):
x 0 0 0
0 y 0 0
0 0 z 0
0 0 0 1
All matrix fields are only set if initM is true.
m - 4x4 matrix in column-major order (also result)m_offset - offset in given array m, i.e. start of the 4x4 matrixinitM - if true, given matrix will be initialized w/ identity matrix,
otherwise only the diagonal and last-row is set.
The latter can be utilized to share a once identity set matrix
for scaling
and translation,
while leaving the other fields untouched for performance reasons.public static float[] makeScale(float[] m,
boolean initM,
float sx,
float sy,
float sz)
Scale matrix (Any Order):
x 0 0 0
0 y 0 0
0 0 z 0
0 0 0 1
All matrix fields are only set if initM is true.
m - 4x4 matrix in column-major order (also result)initM - if true, given matrix will be initialized w/ identity matrix,
otherwise only the diagonal and last-row is set.
The latter can be utilized to share a once identity set matrix
for scaling
and translation,
while leaving the other fields untouched for performance reasons.public static float[] makeRotationAxis(float[] m,
int m_offset,
float angrad,
float x,
float y,
float z,
float[] tmpVec3f)
Rotation matrix (Column Order):
xx(1-c)+c xy(1-c)+zs xz(1-c)-ys 0
xy(1-c)-zs yy(1-c)+c yz(1-c)+xs 0
xz(1-c)+ys yz(1-c)-xs zz(1-c)+c 0
0 0 0 1
All matrix fields are set.
m - 4x4 matrix in column-major order (also result)m_offset - offset in given array m, i.e. start of the 4x4 matrixpublic static float[] makeRotationEuler(float[] m,
int m_offset,
float bankX,
float headingY,
float attitudeZ)
The rotations are applied in the given order:
All matrix fields are set.
m - 4x4 matrix in column-major order (also result)m_offset - offset in given array m, i.e. start of the 4x4 matrixbankX - the Euler pitch angle in radians. (rotation about the X axis)headingY - the Euler yaw angle in radians. (rotation about the Y axis)attitudeZ - the Euler roll angle in radians. (rotation about the Z axis)Implementation does not use Quaternion and hence is exposed to Gimbal-Lock
public static float[] makeOrtho(float[] m,
int m_offset,
boolean initM,
float left,
float right,
float bottom,
float top,
float zNear,
float zFar)
Ortho matrix (Column Order):
2/dx 0 0 0
0 2/dy 0 0
0 0 2/dz 0
tx ty tz 1
All matrix fields are only set if initM is true.
m - 4x4 matrix in column-major order (also result)m_offset - offset in given array m, i.e. start of the 4x4 matrixinitM - if true, given matrix will be initialized w/ identity matrix,
otherwise only the orthogonal fields are set.left - right - bottom - top - zNear - zFar - public static float[] makeFrustum(float[] m,
int m_offset,
boolean initM,
float left,
float right,
float bottom,
float top,
float zNear,
float zFar)
throws GLException
Frustum matrix (Column Order):
2*zNear/dx 0 0 0
0 2*zNear/dy 0 0
A B C -1
0 0 D 0
All matrix fields are only set if initM is true.
m - 4x4 matrix in column-major order (also result)m_offset - offset in given array m, i.e. start of the 4x4 matrixinitM - if true, given matrix will be initialized w/ identity matrix,
otherwise only the frustum fields are set.left - right - bottom - top - zNear - zFar - GLException - if zNear <= 0 or zFar <= zNear
or left == right, or bottom == top.public static float[] makePerspective(float[] m,
int m_off,
boolean initM,
float fovy_rad,
float aspect,
float zNear,
float zFar)
throws GLException
frustum
matrix based on given parameters.
All matrix fields are only set if initM is true.
m - 4x4 matrix in column-major order (also result)m_offset - offset in given array m, i.e. start of the 4x4 matrixinitM - if true, given matrix will be initialized w/ identity matrix,
otherwise only the frustum fields are set.fovy_rad - angle in radiansaspect - aspect ratio width / heightzNear - zFar - GLException - if zNear <= 0 or zFar <= zNearmakeFrustum(float[], int, boolean, float, float, float, float, float, float)public static float[] makePerspective(float[] m,
int m_offset,
boolean initM,
FovHVHalves fovhv,
float zNear,
float zFar)
throws GLException
frustum
matrix based on given parameters.
All matrix fields are only set if initM is true.
m - 4x4 matrix in column-major order (also result)m_offset - offset in given array m, i.e. start of the 4x4 matrixinitM - if true, given matrix will be initialized w/ identity matrix,
otherwise only the frustum fields are set.fovhv - FovHVHalves field of view in both directions, may not be centered, either in radians or tangentzNear - zFar - GLException - if zNear <= 0 or zFar <= zNearmakeFrustum(float[], int, boolean, float, float, float, float, float, float),
Frustum.updateByFovDesc(float[], int, boolean, Frustum.FovDesc)public static float[] makeLookAt(float[] m,
int m_offset,
float[] eye,
int eye_offset,
float[] center,
int center_offset,
float[] up,
int up_offset,
float[] mat4Tmp)
Consist out of two matrix multiplications:
R = L x T,
with L for look-at matrix and
T for eye translation.
Result R can be utilized for modelview multiplication, i.e.
M = M x R,
with M being the modelview matrix.
All matrix fields are set.
m - 4x4 matrix in column-major order, result onlym_offset - offset in given array m, i.e. start of the 4x4 matrixeye - 3 component eye vectoreye_offset - center - 3 component center vectorcenter_offset - up - 3 component up vectorup_offset - mat4Tmp - temp float[16] storagem for chainingpublic static float[] makePick(float[] m,
int m_offset,
float x,
float y,
float deltaX,
float deltaY,
int[] viewport,
int viewport_offset,
float[] mat4Tmp)
Traditional gluPickMatrix implementation.
Consist out of two matrix multiplications:
R = T x S,
with T for viewport translation matrix and
S for viewport scale matrix.
Result R can be utilized for projection multiplication, i.e.
P = P x R,
with P being the projection matrix.
To effectively use the generated pick matrix for picking,
call makePick
and multiply a custom perspective matrix
by this pick matrix. Then you may load the result onto the perspective matrix stack.
All matrix fields are set.
m - 4x4 matrix in column-major order, result onlym_offset - offset in given array m, i.e. start of the 4x4 matrixx - the center x-component of a picking region in window coordinatesy - the center y-component of a picking region in window coordinatesdeltaX - the width of the picking region in window coordinates.deltaY - the height of the picking region in window coordinates.viewport - 4 component viewport vectorviewport_offset - mat4Tmp - temp float[16] storagem for chaining or null if either delta value is <= zero.public static float[] transposeMatrix(float[] msrc,
int msrc_offset,
float[] mres,
int mres_offset)
msrc - 4x4 matrix in column-major order, the sourcemsrc_offset - offset in given array msrc, i.e. start of the 4x4 matrixmres - 4x4 matrix in column-major order, the resultmres_offset - offset in given array mres, i.e. start of the 4x4 matrixpublic static float[] transposeMatrix(float[] msrc,
float[] mres)
msrc - 4x4 matrix in column-major order, the sourcemres - 4x4 matrix in column-major order, the resultpublic static float matrixDeterminant(float[] m,
int m_offset)
m - 4x4 matrix in column-major order, the sourcem_offset - offset in given array m, i.e. start of the 4x4 matrixpublic static float matrixDeterminant(float[] m)
m - 4x4 matrix in column-major order, the sourcepublic static float[] invertMatrix(float[] msrc,
int msrc_offset,
float[] mres,
int mres_offset)
Returns null if inversion is not possible,
e.g. matrix is singular due to a bad matrix.
msrc - 4x4 matrix in column-major order, the sourcemsrc_offset - offset in given array msrc, i.e. start of the 4x4 matrixmres - 4x4 matrix in column-major order, the result - may be msrc (in-place)mres_offset - offset in given array mres, i.e. start of the 4x4 matrix - may be msrc_offset (in-place)null. See above.public static float[] invertMatrix(float[] msrc,
float[] mres)
Returns null if inversion is not possible,
e.g. matrix is singular due to a bad matrix.
msrc - 4x4 matrix in column-major order, the sourcemres - 4x4 matrix in column-major order, the result - may be msrc (in-place)null. See above.public static boolean mapObjToWinCoords(float objx,
float objy,
float objz,
float[] modelMatrix,
int modelMatrix_offset,
float[] projMatrix,
int projMatrix_offset,
int[] viewport,
int viewport_offset,
float[] win_pos,
int win_pos_offset,
float[] vec4Tmp1,
float[] vec4Tmp2)
Traditional gluProject implementation.
objx - objy - objz - modelMatrix - 4x4 modelview matrixmodelMatrix_offset - projMatrix - 4x4 projection matrixprojMatrix_offset - viewport - 4 component viewport vectorviewport_offset - win_pos - 3 component window coordinate, the resultwin_pos_offset - vec4Tmp1 - 4 component vector for temp storagevec4Tmp2 - 4 component vector for temp storagepublic static boolean mapObjToWinCoords(float objx,
float objy,
float objz,
float[] mat4PMv,
int[] viewport,
int viewport_offset,
float[] win_pos,
int win_pos_offset,
float[] vec4Tmp1,
float[] vec4Tmp2)
Traditional gluProject implementation.
objx - objy - objz - mat4PMv - [projection] x [modelview] matrix, i.e. P x Mvviewport - 4 component viewport vectorviewport_offset - win_pos - 3 component window coordinate, the resultwin_pos_offset - vec4Tmp1 - 4 component vector for temp storagevec4Tmp2 - 4 component vector for temp storagepublic static boolean mapWinToObjCoords(float winx,
float winy,
float winz,
float[] modelMatrix,
int modelMatrix_offset,
float[] projMatrix,
int projMatrix_offset,
int[] viewport,
int viewport_offset,
float[] obj_pos,
int obj_pos_offset,
float[] mat4Tmp1,
float[] mat4Tmp2)
Traditional gluUnProject implementation.
winx - winy - winz - modelMatrix - 4x4 modelview matrixmodelMatrix_offset - projMatrix - 4x4 projection matrixprojMatrix_offset - viewport - 4 component viewport vectorviewport_offset - obj_pos - 3 component object coordinate, the resultobj_pos_offset - mat4Tmp1 - 16 component matrix for temp storagemat4Tmp2 - 16 component matrix for temp storagepublic static boolean mapWinToObjCoords(float winx,
float winy,
float winz,
float[] mat4PMvI,
int[] viewport,
int viewport_offset,
float[] obj_pos,
int obj_pos_offset,
float[] vec4Tmp1,
float[] vec4Tmp2)
Traditional gluUnProject implementation.
winx - winy - winz - mat4PMvI - inverse [projection] x [modelview] matrix, i.e. Inv(P x Mv)viewport - 4 component viewport vectorviewport_offset - obj_pos - 3 component object coordinate, the resultobj_pos_offset - vec4Tmp1 - 4 component vector for temp storagevec4Tmp2 - 4 component vector for temp storagepublic static boolean mapWinToObjCoords(float winx,
float winy,
float winz1,
float winz2,
float[] mat4PMvI,
int[] viewport,
int viewport_offset,
float[] obj1_pos,
int obj1_pos_offset,
float[] obj2_pos,
int obj2_pos_offset,
float[] vec4Tmp1,
float[] vec4Tmp2)
winx - winy - winz1 - winz2 - mat4PMvI - inverse [projection] x [modelview] matrix, i.e. Inv(P x Mv)viewport - 4 component viewport vectorviewport_offset - obj1_pos - 3 component object coordinate, the result for winz1obj1_pos_offset - obj2_pos - 3 component object coordinate, the result for winz2obj2_pos_offset - vec4Tmp1 - 4 component vector for temp storagevec4Tmp2 - 4 component vector for temp storagepublic static boolean mapWinToObjCoords(float winx,
float winy,
float winz,
float clipw,
float[] modelMatrix,
int modelMatrix_offset,
float[] projMatrix,
int projMatrix_offset,
int[] viewport,
int viewport_offset,
float near,
float far,
float[] obj_pos,
int obj_pos_offset,
float[] mat4Tmp1,
float[] mat4Tmp2)
Traditional gluUnProject4 implementation.
winx - winy - winz - clipw - modelMatrix - 4x4 modelview matrixmodelMatrix_offset - projMatrix - 4x4 projection matrixprojMatrix_offset - viewport - 4 component viewport vectorviewport_offset - near - far - obj_pos - 4 component object coordinate, the resultobj_pos_offset - mat4Tmp1 - 16 component matrix for temp storagemat4Tmp2 - 16 component matrix for temp storagepublic static boolean mapWinToRay(float winx,
float winy,
float winz0,
float winz1,
float[] modelMatrix,
int modelMatrix_offset,
float[] projMatrix,
int projMatrix_offset,
int[] viewport,
int viewport_offset,
Ray ray,
float[] mat4Tmp1,
float[] mat4Tmp2,
float[] vec4Tmp2)
Ray. The resulting Ray maybe used for picking
using a bounding box.
Notes for picking winz0 and winz1:
winx - winy - winz0 - winz1 - modelMatrix - 4x4 modelview matrixmodelMatrix_offset - projMatrix - 4x4 projection matrixprojMatrix_offset - viewport - 4 component viewport vectorviewport_offset - ray - storage for the resulting Raymat4Tmp1 - 16 component matrix for temp storagemat4Tmp2 - 16 component matrix for temp storagevec4Tmp2 - 4 component vector for temp storagepublic static float[] multMatrix(float[] a,
int a_off,
float[] b,
int b_off,
float[] d,
int d_off)
a - 4x4 matrix in column-major orderb - 4x4 matrix in column-major orderd - result a*b in column-major orderpublic static float[] multMatrix(float[] a,
float[] b,
float[] d)
a - 4x4 matrix in column-major orderb - 4x4 matrix in column-major orderd - result a*b in column-major orderpublic static float[] multMatrix(float[] a,
int a_off,
float[] b,
int b_off)
a - 4x4 matrix in column-major order (also result)b - 4x4 matrix in column-major orderpublic static float[] multMatrix(float[] a,
float[] b)
a - 4x4 matrix in column-major order (also result)b - 4x4 matrix in column-major orderpublic static void multMatrix(FloatBuffer a, FloatBuffer b, float[] d)
a - 4x4 matrix in column-major orderb - 4x4 matrix in column-major orderd - result a*b in column-major orderpublic static void multMatrix(FloatBuffer a, FloatBuffer b)
a - 4x4 matrix in column-major order (also result)b - 4x4 matrix in column-major orderpublic static float[] multMatrixVec(float[] m_in,
int m_in_off,
float[] v_in,
int v_in_off,
float[] v_out,
int v_out_off)
m_in - 4x4 matrix in column-major orderm_in_off - v_in - 4-component column-vectorv_out - m_in * v_inpublic static float[] multMatrixVec(float[] m_in,
float[] v_in,
float[] v_out)
m_in - 4x4 matrix in column-major orderm_in_off - v_in - 4-component column-vectorv_out - m_in * v_inpublic static void multMatrixVec(FloatBuffer m_in, float[] v_in, float[] v_out)
m_in - 4x4 matrix in column-major orderv_in - 4-component column-vectorv_out - m_in * v_inpublic static float[] copyMatrixColumn(float[] m_in,
int m_in_off,
int column,
float[] v_out,
int v_out_off)
v_out may be 3 or 4 components long, hence the 4th row may not be stored.
m_in - input column-major matrixm_in_off - offset to input matrixcolumn - named column to copyv_out - the column-vector storage, at least 3 components longv_out_off - offset to storagepublic static float[] copyMatrixRow(float[] m_in,
int m_in_off,
int row,
float[] v_out,
int v_out_off)
v_out may be 3 or 4 components long, hence the 4th column may not be stored.
m_in - input column-major matrixm_in_off - offset to input matrixrow - named row to copyv_out - the row-vector storage, at least 3 components longv_out_off - offset to storagepublic static StringBuilder matrixRowToString(StringBuilder sb, String f, FloatBuffer a, int aOffset, int rows, int columns, boolean rowMajorOrder, int row)
sb - optional passed StringBuilder instance to be usedf - the format string of one floating point, i.e. "%10.5f", see Formattera - mxn matrix (rows x columns)aOffset - offset to a's current positionrows - columns - rowMajorOrder - if true floats are layed out in row-major-order, otherwise column-major-order (OpenGL)row - row number to printpublic static StringBuilder matrixRowToString(StringBuilder sb, String f, float[] a, int aOffset, int rows, int columns, boolean rowMajorOrder, int row)
sb - optional passed StringBuilder instance to be usedf - the format string of one floating point, i.e. "%10.5f", see Formattera - mxn matrix (rows x columns)aOffset - offset to a's current positionrows - columns - rowMajorOrder - if true floats are layed out in row-major-order, otherwise column-major-order (OpenGL)row - row number to printpublic static StringBuilder matrixToString(StringBuilder sb, String rowPrefix, String f, FloatBuffer a, int aOffset, int rows, int columns, boolean rowMajorOrder)
sb - optional passed StringBuilder instance to be usedrowPrefix - optional prefix for each rowf - the format string of one floating point, i.e. "%10.5f", see Formattera - mxn matrix (rows x columns)aOffset - offset to a's current positionrows - columns - rowMajorOrder - if true floats are layed out in row-major-order, otherwise column-major-order (OpenGL)public static StringBuilder matrixToString(StringBuilder sb, String rowPrefix, String f, float[] a, int aOffset, int rows, int columns, boolean rowMajorOrder)
sb - optional passed StringBuilder instance to be usedrowPrefix - optional prefix for each rowf - the format string of one floating point, i.e. "%10.5f", see Formattera - mxn matrix (rows x columns)aOffset - offset to a's current positionrows - columns - rowMajorOrder - if true floats are layed out in row-major-order, otherwise column-major-order (OpenGL)public static StringBuilder matrixToString(StringBuilder sb, String rowPrefix, String f, FloatBuffer a, int aOffset, FloatBuffer b, int bOffset, int rows, int columns, boolean rowMajorOrder)
sb - optional passed StringBuilder instance to be usedrowPrefix - optional prefix for each rowf - the format string of one floating point, i.e. "%10.5f", see Formattera - 4x4 matrix in column major order (OpenGL)aOffset - offset to a's current positionb - 4x4 matrix in column major order (OpenGL)bOffset - offset to a's current positionrows - columns - rowMajorOrder - if true floats are layed out in row-major-order, otherwise column-major-order (OpenGL)public static StringBuilder matrixToString(StringBuilder sb, String rowPrefix, String f, float[] a, int aOffset, float[] b, int bOffset, int rows, int columns, boolean rowMajorOrder)
sb - optional passed StringBuilder instance to be usedrowPrefix - optional prefix for each rowf - the format string of one floating point, i.e. "%10.5f", see Formattera - 4x4 matrix in column major order (OpenGL)aOffset - offset to a's current positionb - 4x4 matrix in column major order (OpenGL)bOffset - offset to a's current positionrows - columns - rowMajorOrder - if true floats are layed out in row-major-order, otherwise column-major-order (OpenGL)public static float getMachineEpsilon()
The machine Epsilon value is computed once.
On a reference machine the result was EPSILON in 23 iterations.
EPSILONpublic static boolean isEqual(float a,
float b)
Implementation considers following corner cases:
isEqual(float, float, float)public static boolean isEqual(float a,
float b,
float epsilon)
epsilon.
Implementation considers following corner cases:
EPSILONpublic static int compare(float a,
float b)
Implementation considers following corner cases:
compare(float, float, float)public static int compare(float a,
float b,
float epsilon)
epsilon.
Implementation considers following corner cases:
EPSILONpublic static boolean isZero(float a,
float epsilon)
epsilon.EPSILONpublic static float abs(float a)
public static float pow(float a,
float b)
public static float sin(float a)
public static float asin(float a)
public static float cos(float a)
public static float acos(float a)
public static float tan(float a)
public static float atan(float a)
public static float atan2(float y,
float x)
public static float sqrt(float a)
public static float getZBufferEpsilon(int zBits,
float z,
float zNear)
return z * z / ( zNear * (1<<zBits) - z )
zBits - number of bits of Z precision, i.e. z-buffer depthz - distance from the eye to the objectzNear - distance from eye to near clip planepublic static int getZBufferValue(int zBits,
float z,
float zNear,
float zFar)
float a = zFar / ( zFar - zNear ) float b = zFar * zNear / ( zNear - zFar ) return (int) ( (1<<zBits) * ( a + b / z ) )
zBits - number of bits of Z precision, i.e. z-buffer depthz - distance from the eye to the objectzNear - distance from eye to near clip planezFar - distance from eye to far clip planepublic static float getOrthoWinZ(float orthoZ,
float zNear,
float zFar)
Copyright 2010 JogAmp Community.