/**
* Copyright (c) 2013, Mattias Andrée
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
* ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
package v;
/**
* Orthonormalised vector maths
*/
public class VMaths
{
public static final float[][] UNIT = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
public static float[] createRotation(String side)
{
return createRotation(side, UNIT);
}
public static float[] createRotation(String side, float[][] proj)
{
switch (side.toLowerCase())
{
case "x":
case "xz":
case "zx":
return mul(-1, proj[1]);
case "y":
case "yz":
case "zy":
return mul(-1, proj[0]);
case "xy":
case "yx":
return proj[2];
}
return null;
}
public static float[][] createRotation(String side, float thetaDegrees)
{
switch (side.toLowerCase())
{
case "x":
case "xz":
case "zx":
return createRotation( 0f, -1f, 0f, thetaDegrees);
case "y":
case "yz":
case "zy":
return createRotation(-1f, 0f, 0f, thetaDegrees);
case "xy":
case "yx":
return createRotation( 0f, 0f, +1f, thetaDegrees);
}
return null;
}
public static float[][] createRotation(float x, float y, float z, float thetaDegrees)
{
float theta = thetaDegrees * (float)(Math.PI) / 180f;
float[][] m = new float[3][3];
float cos = (float)(Math.cos(theta));
float sin = (float)(Math.sin(theta));
float _cos = 1f - cos;
m[0][0] = x * x * _cos + cos;
m[1][0] = x * y * _cos + z * sin;
m[2][0] = x * z * _cos - y * sin;
m[0][1] = y * x * _cos - z * sin;
m[1][1] = y * y * _cos + cos;
m[2][1] = y * z * _cos + x * sin;
m[0][2] = z * x * _cos + y * sin;
m[1][2] = z * y * _cos - x * sin;
m[2][2] = z * z * _cos + cos;
return m;
}
public static float[][] createRotation(float[] v, float thetaDegrees)
{
return createRotation(v[0], v[1], v[2], thetaDegrees);
}
public static float[] mul(float[][] m, float[] v)
{
int n, k = v.length;
float[] rc = new float[n = m.length];
for (int r = 0; r < n; r++)
for (int i = 0; i < k; i++)
rc[r] += m[r][i] * v[i];
return rc;
}
public static float[] mul(float[][] m, float x, float y, float z)
{
int n;
float[] rc = new float[n = m.length];
for (int i = 0; i < n; i++)
rc[i] = m[i][0] * x
+ m[i][1] * y
+ m[i][2] * z;
return rc;
}
public static float[][] mul(float[][] a, float[][] b)
{
int n, m, k = b.length;
float[][] rc = new float[n = a.length][m = b[0].length];
for (int r = 0; r < n; r++)
for (int c = 0; c < m; c++)
for (int i = 0; i < k; i++)
rc[r][c] += a[i][r] * b[c][i];
return rc;
}
public static float[][] mul(float a, float[][] b)
{
int n, m;
float[][] rc = new float[n = b.length][m = b[0].length];
for (int r = 0; r < n; r++)
for (int c = 0; c < m; c++)
rc[r][c] = a * b[r][c];
return rc;
}
public static float[] mul(float a, float[] b)
{
int n;
float[] rc = new float[n = b.length];
for (int r = 0; r < n; r++)
rc[r] = a * b[r];
return rc;
}
public static float[][] add(float[][] a, float[][] b)
{
int n, m;
float[][] rc = new float[n = a.length][m = b[0].length];
for (int r = 0; r < n; r++)
for (int c = 0; c < m; c++)
rc[r][c] = a[r][c] + b[r][c];
return rc;
}
public static float[] add(float[] a, float[] b)
{
int n;
float[] rc = new float[n = a.length];
for (int r = 0; r < n; r++)
rc[r] = a[r] + b[r];
return rc;
}
public static float length(float[] v)
{
int n = v.length;
float length = 0;
for (int r = 0; r < n; r++)
length += v[r] * v[r];
length = (float)Math.sqrt(length);
return length;
}
public static float[] normalise(float[] v)
{
int n;
float[] rc = new float[n = v.length];
float length = length(v);
if (length * length == 0f)
{
for (int r = 0; r < n; r++)
rc[r] = 0;
rc[0] = 1;
}
else
for (int r = 0; r < n; r++)
rc[r] = v[r] / length;
return rc;
}
public static float[][] on_inv(float[][] m)
{
return trans(m);
}
public static float[][] inv(float[][] m)
{
return mul(1f / det(m), trans(m));
}
public static float[][] trans(float[][] m)
{
int x, y;
float[][] rc = new float[y = m[0].length][x = m.length];
for (int r = 0; r < y; r++)
for (int c = 0; c < x; c++)
rc[r][c] = m[c][r];
return rc;
}
public static float det(float[][] m)
{
float rc = 0;
int mul = 1;
int n = m.length;
if (n == 0) return 1;
if (n == 1) return m[0][0];
for (int i = 0; i < n; i++)
{
float[][] sub = new float[n - 1][n - 1];
for (int y = 0; y < n - 1; y++)
for (int x = 0; x < n - 1; x++)
sub[y][x] = m[y + 1][x < i ? x : x + 1];
rc += mul * det(sub);
mul *= -1;
}
return rc;
}
}
