Implementation of a 4x4 matrix suited for use in a 2D and 3D graphics rendering engine
/*
* (C) 2004 - Geotechnical Software Services
*
* This code is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This code is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this program; if not, write to the Free
* Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
* MA 02111-1307, USA.
*/
//package no.geosoft.cc.geometry;
/**
* Implementation of a 4x4 matrix suited for use in a 2D and 3D
* graphics rendering engine.
*
* @author <a href="mailto:jacob.dreyer@geosoft.no">Jacob Dreyer</a>
*/
public class Matrix4x4
{
private double[] m_; // of 16
/**
* Construct a 4x4 identity matrix.
*/
public Matrix4x4()
{
initialize();
setIdentity();
}
/**
* Construct a 4x4 matrix with the specified element values.
*
* @param m Array of 16 matrix elements, m00, m01, etc.
*/
public Matrix4x4 (double[] m)
{
initialize();
set (m);
}
/**
* Constrauct a 4x4 matrix as a copy of the specified matrix.
*
* @param matrix Matrix to copy.
*/
public Matrix4x4 (Matrix4x4 matrix)
{
initialize();
set (matrix);
}
/**
* Construct a 4x4 matrix with the specified values.
*
* @param m00 Value of element m[0,0].
* @param m01 Value of element m[0,1].
* @param m02 Value of element m[0,2].
* @param m03 Value of element m[0,3].
* @param m10 Value of element m[1,0].
* @param m11 Value of element m[1,1].
* @param m12 Value of element m[1,2].
* @param m13 Value of element m[1,3].
* @param m20 Value of element m[2,0].
* @param m21 Value of element m[2,1].
* @param m22 Value of element m[2,2].
* @param m23 Value of element m[2,3].
* @param m30 Value of element m[3,0].
* @param m31 Value of element m[3,1].
* @param m32 Value of element m[3,2].
* @param m33 Value of element m[3,3].
*/
public Matrix4x4 (double m00, double m01, double m02, double m03,
double m10, double m11, double m12, double m13,
double m20, double m21, double m22, double m23,
double m30, double m31, double m32, double m33)
{
initialize();
set (m00, m01, m02, m03,
m10, m11, m12, m13,
m20, m21, m22, m23,
m30, m31, m32, m33);
}
/**
* Initialize the matrix.
*/
private void initialize()
{
m_ = new double[16];
}
/**
* Make an identity matrix out of this 4x4 matrix.
*/
public void setIdentity()
{
for (int i=0; i<4; i++)
for (int j=0; j<4; j++)
m_[i*4 + j] = i == j ? 1.0 : 0.0;
}
/**
* Set the value of this 4x4matrix according to the specified
* matrix
*
* @param matrix Matrix to copy.
*/
public void set (Matrix4x4 matrix)
{
for (int i=0; i<16; i++)
m_[i] = matrix.m_[i];
}
/**
* Set the values of this 4x4 matrix.
*
* @param m Array of 16 matrix elements, m00, m01, etc.
*/
public void set (double[] m)
{
for (int i=0; i<16; i++)
m_[i] = m[i];
}
/**
* Set the values of this 4x4 matrix.
*
* @param m00 Value of element m[0,0].
* @param m01 Value of element m[0,1].
* @param m02 Value of element m[0,2].
* @param m03 Value of element m[0,3].
* @param m10 Value of element m[1,0].
* @param m11 Value of element m[1,1].
* @param m12 Value of element m[1,2].
* @param m13 Value of element m[1,3].
* @param m20 Value of element m[2,0].
* @param m21 Value of element m[2,1].
* @param m22 Value of element m[2,2].
* @param m23 Value of element m[2,3].
* @param m30 Value of element m[3,0].
* @param m31 Value of element m[3,1].
* @param m32 Value of element m[3,2].
* @param m33 Value of element m[3,3].
*/
public void set (double m00, double m01, double m02, double m03,
double m10, double m11, double m12, double m13,
double m20, double m21, double m22, double m23,
double m30, double m31, double m32, double m33)
{
m_[0] = m00;
m_[1] = m01;
m_[2] = m02;
m_[3] = m03;
m_[4] = m10;
m_[5] = m11;
m_[6] = m12;
m_[7] = m13;
m_[8] = m20;
m_[9] = m21;
m_[10] = m22;
m_[11] = m23;
m_[12] = m30;
m_[13] = m31;
m_[14] = m32;
m_[15] = m33;
}
/**
* Return the values of this 4x4 matrix.
*
* @return Array ov values: m00, m01, etc.
*/
public double[] get()
{
return m_;
}
/**
* Check if this 4x4 matrix equals the specified object.
*
* @param object Object to check.
* @return True if the two are equal, false otherwise.
* @throws ClassCastException if object is not of type Matrix4x4.
*/
public boolean equals (Object object)
{
Matrix4x4 matrix = (Matrix4x4) object;
for (int i=0; i<16; i++)
if (m_[i] != matrix.m_[i]) return false;
return true;
}
/**
* Return matrix element [i,j].
*
* @param i Row of element to get (first row is 0).
* @param j Column of element to get (first column is 0).
* @return Element at specified position.
* @throws ArrayOutOfBoundsException
*/
public double getElement (int i, int j)
{
return m_[i*4 + j];
}
/**
* Set specified matrix element.
*
* @param i Row of element to set (first row is 0).
* @param j Column of element to set (first column is 0).
* @param value New element value.
* @throws ArrayOutOfBoundsException
*/
public void setElement (int i, int j, double value)
{
m_[i*4 + j] = value;
}
/**
* Add the specified 4x4 matrix to this matrix.
*
* @param matrix Matrix to add.
*/
public void add (Matrix4x4 matrix)
{
for (int i=0; i<4; i++)
for (int j=0; j<4; j++)
m_[i*4 + j] += matrix.m_[i*4 + j];
}
/**
* Add two matrices and return the result matrix.
*
* @param m1 First matrix to add.
* @param m2 Second matrix to add.
* @return Sum m1 + m2.
*/
public static Matrix4x4 add (Matrix4x4 m1, Matrix4x4 m2)
{
Matrix4x4 m = new Matrix4x4 (m1);
m.add (m2);
return m;
}
/**
* Multiply this 4x4 matrix with the specified matrix and
* store the result in this 4x4 matrix.
*
* @param matrix Matrix to multiply with.
*/
public void multiply (Matrix4x4 matrix)
{
Matrix4x4 product = new Matrix4x4();
for (int i = 0; i < 16; i += 4) {
for (int j = 0; j < 4; j++) {
product.m_[i + j] = 0.0;
for (int k = 0; k < 4; k++)
product.m_[i + j] += m_[i + k] * matrix.m_[k*4 + j];
}
}
set (product);
}
/**
* Multiply two matrices and return the result matrix.
*
* @param m1 First matrix to multiply.
* @param m2 Second matrix to multiply.
* @return Product m1 * m2.
*/
public static Matrix4x4 multiply (Matrix4x4 m1, Matrix4x4 m2)
{
Matrix4x4 m = new Matrix4x4 (m1);
m.multiply (m2);
return m;
}
/**
* Multiply this 4x4 matrix with the specified vector.
*
* @param vector4 Vector to multiply with.
* @return Result of operation.
*/
public Vector4 multiply (Vector4 vector4)
{
Vector4 product = new Vector4();
for (int i = 0; i < 4; i++) {
double value = 0.0;
for (int j = 0; j < 4; j++)
value += getElement(i, j) * vector4.getElement (j);
product.setElement (i, value);
}
return product;
}
/**
* Transform one coordinate using this 4x4 matrix.
*
* @param point [x0,y0,z0]
* @return Result of operation: [x0',y0',z0']
*/
public double[] transformPoint (double[] point)
{
double[] result = new double[3];
result[0] = point[0] * m_[0] +
point[1] * m_[4] +
point[2] * m_[8] + m_[12];
result[1] = point[0] * m_[1] +
point[1] * m_[5] +
point[2] * m_[9] + m_[13];
result[2] = point[0] * m_[2] +
point[1] * m_[6] +
point[2] * m_[10] + m_[14];
return result;
}
/**
* Transform a set of 3D coordinates using this 4x4 matrix.
* The result of the operation is put back in the original array.
*
* @param point Points to transform [x0,y0,z0,x1,y1,z1,...]
*/
public void transformPoints (double[] points)
{
for (int i = 0; i < points.length; i += 3) {
double x = points[i + 0] * m_[0] +
points[i + 1] * m_[4] +
points[i + 2] * m_[8] + m_[12];
double y = points[i + 0] * m_[1] +
points[i + 1] * m_[5] +
points[i + 2] * m_[9] + m_[13];
double z = points[i + 0] * m_[2] +
points[i + 1] * m_[6] +
points[i + 2] * m_[10] + m_[14];
points[i + 0] = x;
points[i + 1] = y;
points[i + 2] = z;
}
}
/**
* Transform a set of 2D (x,y) coordinates using this 4x4 matrix.
* The result of the operation is put back in the original array
* rounded to the nearest integer.
*
* @param points Points to transform [x0,y0,x1,y1,...].
*/
public void transformXyPoints (double[] points)
{
for (int i = 0; i < points.length; i += 2) {
double x = points[i + 0] * m_[0] +
points[i + 1] * m_[4] + m_[12];
double y = points[i + 0] * m_[1] +
points[i + 1] * m_[5] + m_[13];
points[i + 0] = x;
points[i + 1] = y;
}
}
/**
* Transform a set of 3D coordinates using this 4x4 matrix.
* The result of the operation is put back in the original array.
*
* @param points Points to transform [x0,y0,z0,x1,y1,z1,...].
*/
public void transformPoints (int[] points)
{
for (int i = 0; i < points.length; i += 3) {
double x = points[i + 0] * m_[0] +
points[i + 1] * m_[4] +
points[i + 2] * m_[8] + m_[12];
double y = points[i + 0] * m_[1] +
points[i + 1] * m_[5] +
points[i + 2] * m_[9] + m_[13];
double z = points[i + 0] * m_[2] +
points[i + 1] * m_[6] +
points[i + 2] * m_[10] + m_[14];
points[i + 0] = (int) Math.round (x);
points[i + 1] = (int) Math.round (y);
points[i + 2] = (int) Math.round (z);
}
}
/**
* Transform a set of 2D (x,y) coordinates using this 4x4 matrix.
* The result of the operation is put back in the original array
* rounded to the nearest integer.
*
* @param points Points to transform [x0,y0,x1,y1,...].
*/
public void transformXyPoints (int[] points)
{
for (int i = 0; i < points.length; i += 2) {
double x = points[i + 0] * m_[0] +
points[i + 1] * m_[4] + m_[12];
double y = points[i + 0] * m_[1] +
points[i + 1] * m_[5] + m_[13];
points[i + 0] = (int) Math.round (x);
points[i + 1] = (int) Math.round (y);
}
}
/**
* Apply specified translation to this 4x4 matrix.
*
* @param dx x translation.
* @param dy y translation.
* @param dz z translation.
*/
public void translate (double dx, double dy, double dz)
{
Matrix4x4 translationMatrix = new Matrix4x4();
translationMatrix.setElement (3, 0, dx);
translationMatrix.setElement (3, 1, dy);
translationMatrix.setElement (3, 2, dz);
multiply (translationMatrix);
}
/**
* Apply specified XY translation to this 4x4 matrix.
*
* @param dx x translation.
* @param dy y translation.
*/
public void translate (double dx, double dy)
{
translate (dx, dy, 0.0);
}
/**
* Apply rotation around X axis to this matrix.
*
* @param angle Angle to rotate [radians].
*/
public void rotateX (double angle)
{
Matrix4x4 rotationMatrix = new Matrix4x4();
double cosAngle = Math.cos (angle);
double sinAngle = Math.sin (angle);
rotationMatrix.setElement (1, 1, cosAngle);
rotationMatrix.setElement (1, 2, sinAngle);
rotationMatrix.setElement (2, 1, -sinAngle);
rotationMatrix.setElement (2, 2, cosAngle);
multiply (rotationMatrix);
}
/**
* Apply rotation around Y axis to this matrix.
*
* @param angle Angle to rotate [radians].
*/
public void rotateY (double angle)
{
Matrix4x4 rotationMatrix = new Matrix4x4();
double cosAngle = Math.cos (angle);
double sinAngle = Math.sin (angle);
rotationMatrix.setElement (0, 0, cosAngle);
rotationMatrix.setElement (0, 2, -sinAngle);
rotationMatrix.setElement (2, 0, sinAngle);
rotationMatrix.setElement (2, 2, cosAngle);
multiply (rotationMatrix);
}
/**
* Apply rotation around z axis to this matrix.
*
* @param angle Angle to rotate [radians].
*/
public void rotateZ (double angle)
{
Matrix4x4 rotationMatrix = new Matrix4x4();
double cosAngle = Math.cos (angle);
double sinAngle = Math.sin (angle);
rotationMatrix.setElement (0, 0, cosAngle);
rotationMatrix.setElement (0, 1, sinAngle);
rotationMatrix.setElement (1, 0, -sinAngle);
rotationMatrix.setElement (1, 1, cosAngle);
multiply (rotationMatrix);
}
/**
* Apply rotation around an arbitrary axis.
*
* Ref: http://www.swin.edu.au/astronomy/pbourke/geometry/rotate/
* (but be aware of errors, corrected here)
*
* @param angle Angle to rotate [radians]
* @param p0 First point defining the axis (x,y,z)
* @param p1 Second point defining the axis (x,y,z)
*/
public void rotate (double angle, double[] p0, double[] p1)
{
// Represent axis of rotation by a unit vector [a,b,c]
double a = p1[0] - p0[0];
double b = p1[1] - p0[1];
double c = p1[2] - p0[2];
double length = Math.sqrt (a*a + b*b + c*c);
a /= length;
b /= length;
c /= length;
double d = Math.sqrt (b*b + c*c);
// Coefficients used for step 2 matrix
double e = d == 0.0 ? 1.0 : c / d;
double f = d == 0.0 ? 0.0 : b / d;
// Coefficients used for the step 3 matrix
double k = d;
double l = a;
// Coefficients for the step 5 matrix (inverse of step 3)
double m = d / (a*a + d*d);
double n = a / (a*a + d*d);
// Coefficients for the step 4 matrix
double cosAngle = Math.cos (angle);
double sinAngle = Math.sin (angle);
//
// Step 1
//
Matrix4x4 step1 = new Matrix4x4();
step1.setElement (3, 0, -p0[0]);
step1.setElement (3, 1, -p0[1]);
step1.setElement (3, 2, -p0[2]);
//
// Step 2
//
Matrix4x4 step2 = new Matrix4x4();
step2.setElement (1, 1, e);
step2.setElement (1, 2, f);
step2.setElement (2, 1, -f);
step2.setElement (2, 2, e);
//
// Step 3
//
Matrix4x4 step3 = new Matrix4x4();
step3.setElement (0, 0, k);
step3.setElement (0, 2, l);
step3.setElement (2, 0, -l);
step3.setElement (2, 2, k);
//
// Step 4
//
Matrix4x4 step4 = new Matrix4x4();
step4.setElement (0, 0, cosAngle);
step4.setElement (0, 1, sinAngle);
step4.setElement (1, 0, -sinAngle);
step4.setElement (1, 1, cosAngle);
//
// Step 5 (inverse of step 3)
//
Matrix4x4 step5 = new Matrix4x4();
step5.setElement (0, 0, m);
step5.setElement (0, 2, -n);
step5.setElement (2, 0, n);
step5.setElement (2, 2, m);
//
// Step 6 (inverse of step 2)
//
Matrix4x4 step6 = new Matrix4x4();
step6.setElement (1, 1, e);
step6.setElement (1, 2, -f);
step6.setElement (2, 1, f);
step6.setElement (2, 2, e);
//
// Step 7 (inverse of step 1)
//
Matrix4x4 step7 = new Matrix4x4();
step7.setElement (3, 0, p0[0]);
step7.setElement (3, 1, p0[1]);
step7.setElement (3, 2, p0[2]);
multiply (step1);
multiply (step2);
multiply (step3);
multiply (step4);
multiply (step5);
multiply (step6);
multiply (step7);
}
/**
* Apply scaling (relative to origo) to this 4x4 matrix.
*
* @param xScale Scaling in x direction.
* @param yScale Scaling in y direction.
* @param zScale Scaling in z direction.
*/
public void scale (double xScale, double yScale, double zScale)
{
Matrix4x4 scalingMatrix = new Matrix4x4();
scalingMatrix.setElement (0, 0, xScale);
scalingMatrix.setElement (1, 1, yScale);
scalingMatrix.setElement (2, 2, zScale);
multiply (scalingMatrix);
}
/**
* Apply scaling relative to a fixed point to this 4x4 matrix.
*
* @param xScale Scaling in x direction.
* @param yScale Scaling in y direction.
* @param zScale Scaling in z direction.
* @param fixedPoint Scaling origo.
*/
public void scale (double xScale, double yScale, double zScale,
double[] fixedPoint)
{
Matrix4x4 step1 = new Matrix4x4();
step1.translate (-fixedPoint[0], -fixedPoint[1], -fixedPoint[2]);
Matrix4x4 step2 = new Matrix4x4();
step2.scale (xScale, yScale, zScale);
Matrix4x4 step3 = new Matrix4x4();
step3.translate (fixedPoint[0], fixedPoint[1], fixedPoint[2]);
multiply (step1);
multiply (step2);
multiply (step3);
}
/**
* Invert this 4x4 matrix.
*/
public void invert()
{
double[] tmp = new double[12];
double[] src = new double[16];
double[] dst = new double[16];
// Transpose matrix
for (int i = 0; i < 4; i++) {
src[i + 0] = m_[i*4 + 0];
src[i + 4] = m_[i*4 + 1];
src[i + 8] = m_[i*4 + 2];
src[i + 12] = m_[i*4 + 3];
}
// Calculate pairs for first 8 elements (cofactors)
tmp[0] = src[10] * src[15];
tmp[1] = src[11] * src[14];
tmp[2] = src[9] * src[15];
tmp[3] = src[11] * src[13];
tmp[4] = src[9] * src[14];
tmp[5] = src[10] * src[13];
tmp[6] = src[8] * src[15];
tmp[7] = src[11] * src[12];
tmp[8] = src[8] * src[14];
tmp[9] = src[10] * src[12];
tmp[10] = src[8] * src[13];
tmp[11] = src[9] * src[12];
// Calculate first 8 elements (cofactors)
dst[0] = tmp[0]*src[5] + tmp[3]*src[6] + tmp[4]*src[7];
dst[0] -= tmp[1]*src[5] + tmp[2]*src[6] + tmp[5]*src[7];
dst[1] = tmp[1]*src[4] + tmp[6]*src[6] + tmp[9]*src[7];
dst[1] -= tmp[0]*src[4] + tmp[7]*src[6] + tmp[8]*src[7];
dst[2] = tmp[2]*src[4] + tmp[7]*src[5] + tmp[10]*src[7];
dst[2] -= tmp[3]*src[4] + tmp[6]*src[5] + tmp[11]*src[7];
dst[3] = tmp[5]*src[4] + tmp[8]*src[5] + tmp[11]*src[6];
dst[3] -= tmp[4]*src[4] + tmp[9]*src[5] + tmp[10]*src[6];
dst[4] = tmp[1]*src[1] + tmp[2]*src[2] + tmp[5]*src[3];
dst[4] -= tmp[0]*src[1] + tmp[3]*src[2] + tmp[4]*src[3];
dst[5] = tmp[0]*src[0] + tmp[7]*src[2] + tmp[8]*src[3];
dst[5] -= tmp[1]*src[0] + tmp[6]*src[2] + tmp[9]*src[3];
dst[6] = tmp[3]*src[0] + tmp[6]*src[1] + tmp[11]*src[3];
dst[6] -= tmp[2]*src[0] + tmp[7]*src[1] + tmp[10]*src[3];
dst[7] = tmp[4]*src[0] + tmp[9]*src[1] + tmp[10]*src[2];
dst[7] -= tmp[5]*src[0] + tmp[8]*src[1] + tmp[11]*src[2];
// Calculate pairs for second 8 elements (cofactors)
tmp[0] = src[2]*src[7];
tmp[1] = src[3]*src[6];
tmp[2] = src[1]*src[7];
tmp[3] = src[3]*src[5];
tmp[4] = src[1]*src[6];
tmp[5] = src[2]*src[5];
tmp[6] = src[0]*src[7];
tmp[7] = src[3]*src[4];
tmp[8] = src[0]*src[6];
tmp[9] = src[2]*src[4];
tmp[10] = src[0]*src[5];
tmp[11] = src[1]*src[4];
// Calculate second 8 elements (cofactors)
dst[8] = tmp[0] * src[13] + tmp[3] * src[14] + tmp[4] * src[15];
dst[8] -= tmp[1] * src[13] + tmp[2] * src[14] + tmp[5] * src[15];
dst[9] = tmp[1] * src[12] + tmp[6] * src[14] + tmp[9] * src[15];
dst[9] -= tmp[0] * src[12] + tmp[7] * src[14] + tmp[8] * src[15];
dst[10] = tmp[2] * src[12] + tmp[7] * src[13] + tmp[10]* src[15];
dst[10] -= tmp[3] * src[12] + tmp[6] * src[13] + tmp[11]* src[15];
dst[11] = tmp[5] * src[12] + tmp[8] * src[13] + tmp[11]* src[14];
dst[11] -= tmp[4] * src[12] + tmp[9] * src[13] + tmp[10]* src[14];
dst[12] = tmp[2] * src[10] + tmp[5] * src[11] + tmp[1] * src[9];
dst[12] -= tmp[4] * src[11] + tmp[0] * src[9] + tmp[3] * src[10];
dst[13] = tmp[8] * src[11] + tmp[0] * src[8] + tmp[7] * src[10];
dst[13] -= tmp[6] * src[10] + tmp[9] * src[11] + tmp[1] * src[8];
dst[14] = tmp[6] * src[9] + tmp[11]* src[11] + tmp[3] * src[8];
dst[14] -= tmp[10]* src[11 ] + tmp[2] * src[8] + tmp[7] * src[9];
dst[15] = tmp[10]* src[10] + tmp[4] * src[8] + tmp[9] * src[9];
dst[15] -= tmp[8] * src[9] + tmp[11]* src[10] + tmp[5] * src[8];
// Calculate determinant
double det = src[0]*dst[0] + src[1]*dst[1] + src[2]*dst[2] + src[3]*dst[3];
// Calculate matrix inverse
det = 1.0 / det;
for (int i = 0; i < 16; i++)
m_[i] = dst[i] * det;
}
/**
* Return the inverse of the specified matrix.
*
* @param matrix Matrix to finr the inverse of.
* @return Inverse of the specified matrix.
*/
public static Matrix4x4 inverse (Matrix4x4 matrix)
{
Matrix4x4 m = new Matrix4x4 (matrix);
m.invert();
return m;
}
/**
* Solve the A x = b equation, where A is this 4x4 matrix, b is the
* specified result vector and the returned vector is the unknown x.
*
* @param vector Result vector
* @return Unknown vector.
*/
public Vector4 solve (Vector4 vector)
{
Matrix4x4 inverse = new Matrix4x4 (this);
inverse.invert();
Vector4 result = inverse.multiply (vector);
return result;
}
/**
* Make this 4x4 matrix a world-2-device transformation matrix.
* <p>
* The world system is defined as follows:
*
* <pre>
* w2 o
* |
* |
* |
* w0 o-------o w1
* <pre>
* <p>
* Each point is defined with x,y,z so this system may in effect be
* arbitrary oriented in space, and may include sharing.
* <p>
* The device system is defined as follows:
*
* <pre>
* width
* x0,y0 o-------o
* |
* height |
* |
* o
* </pre>
* <p>
* The matrix maps w2 to (x0,y0), w0 to the lower left corner of the
* device rectangle, and w1 to the lower right corner of the device
* rectangle.
*
* @param w0 x,y,z coordinate of first world position.
* @param w1 x,y,z coordinate of second world position.
* @param w2 x,y,z coordinate of third world position.
* @param x0 X coordinate of upper left corner of device.
* @param y0 Y coordinate of upper left corner of device.
* @param width Width of device
* @param height Height of device.
*/
public void setWorld2DeviceTransform (double[] w0, double[] w1, double[] w2,
int x0, int y0, int width, int height)
{
setIdentity();
double[] x = new double[4];
double[] y = new double[4];
double[] z = new double[4];
// Make direction vectors for new system
x[0] = w2[0]; y[0] = w2[1]; z[0] = w2[2];
x[1] = w1[0] - w0[0]; y[1] = w1[1] - w0[1]; z[1] = w1[2] - w0[2];
x[2] = w0[0] - w2[0]; y[2] = w0[1] - w2[1]; z[2] = w0[2] - w2[2];
x[3] = y[1]*z[2] - z[1]*y[2];
y[3] = z[1]*x[2] - x[1]*z[2];
z[3] = x[1]*y[2] - y[1]*x[2];
// Normalize new z-vector, in case someone needs
// new z-value in addition to device coordinates */
double length = Math.sqrt (x[3]*x[3] + y[3]*y[3] + z[3]*z[3]);
x[3] /= length;
y[3] /= length;
z[3] /= length;
// Translate back to new origin
translate (-x[0], -y[0], -z[0]);
// Multiply with inverse of definition of new coordinate system
double a = y[2]*z[3] - z[2]*y[3];
double b = z[1]*y[3] - y[1]*z[3];
double c = y[1]*z[2] - z[1]*y[2];
double det = x[1]*a + x[2]*b + x[3]*c;
double[] m = new double[16];
m[0] = a / det;
m[1] = b / det;
m[2] = c / det;
m[3] = 0.0;
m[4] = (x[3]*z[2] - x[2]*z[3]) / det;
m[5] = (x[1]*z[3] - x[3]*z[1]) / det;
m[6] = (z[1]*x[2] - x[1]*z[2]) / det;
m[7] = 0.0;
m[8] = (x[2]*y[3] - x[3]*y[2]) / det;
m[9] = (y[1]*x[3] - x[1]*y[3]) / det;
m[10] = (x[1]*y[2] - y[1]*x[2]) / det;
m[11] = 0.0;
m[12] = 0.0;
m[13] = 0.0;
m[14] = 0.0;
m[15] = 1.0;
Matrix4x4 matrix = new Matrix4x4 (m);
multiply (matrix);
// Scale according to height and width of viewport
matrix.setIdentity();
matrix.setElement (0, 0, width);
matrix.setElement (1, 1, height);
multiply (matrix);
// Translate according to origin of viewport
matrix.setIdentity();
matrix.setElement (3, 0, x0);
matrix.setElement (3, 1, y0);
multiply (matrix);
}
/**
* Create a string representation of this matrix.
*
* @return String representing this matrix.
*/
public String toString()
{
String string = new String();
for (int i=0; i<4; i++) {
for (int j=0; j<4; j++)
string += getElement(i,j) + " ";
string += '\n';
}
return string;
}
}
/*
* This code is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This code is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this program; if not, write to the Free
* Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
* MA 02111-1307, USA.
*/
//package no.geosoft.cc.geometry;
/**
* Implementation of a 4-element vector suited for use with
* Matrix4x4
*
* @author <a href="mailto:jacob.dreyer@geosoft.no">Jacob Dreyer</a>
*/
//public
class Vector4
{
private double[] v_;
private void initialize()
{
v_ = new double[4];
for (int i = 0; i < 4; i++)
v_[i] = 0.0;
}
/**
* Create a default 4-element vector (all elements set to 0.0).
*/
public Vector4()
{
initialize();
}
/**
* Create a 4-element vector with the specified values.
*
* @param v1 1st element.
* @param v2 2nd element.
* @param v3 3rd element.
* @param v4 4th element
*/
public Vector4 (double v1, double v2, double v3, double v4)
{
initialize();
set (v1, v2, v3, v4);
}
/**
* Construct a 4-element vector as a copy of the specified vector.
*
* @param vector4
*/
public Vector4 (Vector4 vector4)
{
initialize();
set (vector4);
}
/**
* Set the elements of this vector.
*
* @param v1 1st element.
* @param v2 2nd element.
* @param v3 3rd element.
* @param v4 4th element
*/
public void set (double v1, double v2, double v3, double v4)
{
v_[0] = v1;
v_[1] = v2;
v_[2] = v3;
v_[3] = v4;
}
/**
* Set the elements of this vector according to the specified vector.
*
* @param vector Vector to copy.
*/
public void set (Vector4 vector)
{
for (int i = 0; i < 4; i++)
v_[0] = vector.v_[i];
}
/**
* Check if this 4-element vector equals the specified object.
*
* @return TRue if the two equals, false otherwise.
*/
public boolean equals (Object object)
{
Vector4 vector = (Vector4) object;
return v_[0] == vector.v_[0] &&
v_[1] == vector.v_[1] &&
v_[2] == vector.v_[2] &&
v_[3] == vector.v_[3];
}
/**
* Return the i'th element of this vector.
*
* @param i Index of element to get (first is 0).
* @return i'th element of this vector.
*/
public double getElement (int i)
{
return v_[i];
}
/**
* Set the i'th element of this vector.
*
* @param i Index of element to set (first is 0).
* @param Value to set.
*/
public void setElement (int i, double value)
{
v_[i] = value;
}
/**
* Create a string representation of this vector.
*
* @return String representing this vector.
*/
public String toString()
{
return ("Vector4: [" +
v_[0] + "," + v_[1] + "," + v_[2] + "," + v_[3] + "]");
}
}
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