Java examples for java.lang:Math Vector
Finds the plane equation of a plane given its normal and a point on the plane.
/**/* ww w . j a v a 2s. c o m*/ * Copyright 2010 JogAmp Community. 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 JogAmp Community ``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 JogAmp Community 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. * * The views and conclusions contained in the software and documentation are those of the * authors and should not be interpreted as representing official policies, either expressed * or implied, of JogAmp Community. */ import java.util.ArrayList; public class Main{ /** * Finds the plane equation of a plane given its normal and a point on the plane. * * @param resultV4 vec4 plane equation * @param normalVec3 * @param pVec3 * @return result for chaining */ public static float[] getPlaneVec3(final float[/*4*/] resultV4, final float[] normalVec3, final float[] pVec3) { /** Ax + By + Cz + D == 0 ; D = - ( Ax + By + Cz ) = - ( A*a[0] + B*a[1] + C*a[2] ) = - vec3Dot ( normal, a ) ; */ System.arraycopy(normalVec3, 0, resultV4, 0, 3); resultV4[3] = -dotVec3(normalVec3, pVec3); return resultV4; } /** * This finds the plane equation of a triangle given three vertices. * * @param resultVec4 vec4 plane equation * @param v1 vec3 * @param v2 vec3 * @param v3 vec3 * @param temp1V3 * @param temp2V3 * @return result for chaining */ public static float[] getPlaneVec3(final float[/*4*/] resultVec4, final float[] v1, final float[] v2, final float[] v3, final float[] temp1V3, final float[] temp2V3) { /** Ax + By + Cz + D == 0 ; D = - ( Ax + By + Cz ) = - ( A*a[0] + B*a[1] + C*a[2] ) = - vec3Dot ( normal, a ) ; */ getNormalVec3(resultVec4, v1, v2, v3, temp1V3, temp2V3); resultVec4[3] = -dotVec3(resultVec4, v1); return resultVec4; } /** * Return the dot product of two points * @param vec1 vector 1 * @param vec2 vector 2 * @return the dot product as float */ public static float dotVec3(final float[] vec1, final float[] vec2) { return vec1[0] * vec2[0] + vec1[1] * vec2[1] + vec1[2] * vec2[2]; } /** * Returns the 3d surface normal of a triangle given three vertices. * * @param result vec3 result for normal * @param v1 vec3 * @param v2 vec3 * @param v3 vec3 * @param tmp1Vec3 temp vec3 * @param tmp2Vec3 temp vec3 * @return result for chaining */ public static float[] getNormalVec3(final float[] result, final float[] v1, final float[] v2, final float[] v3, final float[] tmp1Vec3, final float[] tmp2Vec3) { subVec3(tmp1Vec3, v2, v1); subVec3(tmp2Vec3, v3, v1); return normalizeVec3(crossVec3(result, tmp1Vec3, tmp2Vec3)); } /** * Subtracts two vectors, result = v1 - v2 * @param result float[3] result vector, may be either v1 or v2 (in-place) * @param v1 vector 1 * @param v2 vector 2 * @return result vector for chaining */ public static float[] subVec3(final float[] result, final float[] v1, final float[] v2) { result[0] = v1[0] - v2[0]; result[1] = v1[1] - v2[1]; result[2] = v1[2] - v2[2]; return result; } /** * Normalize a vector * @param result output vector, may be vector (in-place) * @param vector input vector * @return normalized output vector * @return result vector for chaining */ public static float[] normalizeVec3(final float[] result, final float[] vector) { final float lengthSq = normSquareVec3(vector); if (FloatUtil.isZero(lengthSq, FloatUtil.EPSILON)) { result[0] = 0f; result[1] = 0f; result[2] = 0f; } else { final float invSqr = 1f / FloatUtil.sqrt(lengthSq); result[0] = vector[0] * invSqr; result[1] = vector[1] * invSqr; result[2] = vector[2] * invSqr; } return result; } /** * Normalize a vector in place * @param vector input vector * @return normalized output vector */ public static float[] normalizeVec3(final float[] vector) { final float lengthSq = normSquareVec3(vector); if (FloatUtil.isZero(lengthSq, FloatUtil.EPSILON)) { vector[0] = 0f; vector[1] = 0f; vector[2] = 0f; } else { final float invSqr = 1f / FloatUtil.sqrt(lengthSq); vector[0] *= invSqr; vector[1] *= invSqr; vector[2] *= invSqr; } return vector; } /** * Normalize a vector in place * @param vector input vector * @return normalized output vector */ public static float[] normalizeVec3(final float[] vector, final int offset) { final float lengthSq = normSquareVec3(vector, offset); if (FloatUtil.isZero(lengthSq, FloatUtil.EPSILON)) { vector[0 + offset] = 0f; vector[1 + offset] = 0f; vector[2 + offset] = 0f; } else { final float invSqr = 1f / FloatUtil.sqrt(lengthSq); vector[0 + offset] *= invSqr; vector[1 + offset] *= invSqr; vector[2 + offset] *= invSqr; } return vector; } /** * cross product vec1 x vec2 * @param v1 vector 1 * @param v2 vector 2 * @return the resulting vector */ public static float[] crossVec3(final float[] result, final float[] v1, final float[] v2) { result[0] = v1[1] * v2[2] - v1[2] * v2[1]; result[1] = v1[2] * v2[0] - v1[0] * v2[2]; result[2] = v1[0] * v2[1] - v1[1] * v2[0]; return result; } /** * cross product vec1 x vec2 * @param v1 vector 1 * @param v2 vector 2 * @return the resulting vector */ public static float[] crossVec3(final float[] r, final int r_offset, final float[] v1, final int v1_offset, final float[] v2, final int v2_offset) { r[0 + r_offset] = v1[1 + v1_offset] * v2[2 + v2_offset] - v1[2 + v1_offset] * v2[1 + v2_offset]; r[1 + r_offset] = v1[2 + v1_offset] * v2[0 + v2_offset] - v1[0 + v1_offset] * v2[2 + v2_offset]; r[2 + r_offset] = v1[0 + v1_offset] * v2[1 + v2_offset] - v1[1 + v1_offset] * v2[0 + v2_offset]; return r; } /** * Return the squared length of a vector, a.k.a the squared <i>norm</i> or squared <i>magnitude</i> */ public static float normSquareVec3(final float[] vec) { return vec[0] * vec[0] + vec[1] * vec[1] + vec[2] * vec[2]; } /** * Return the squared length of a vector, a.k.a the squared <i>norm</i> or squared <i>magnitude</i> */ public static float normSquareVec3(final float[] vec, final int offset) { float v = vec[0 + offset]; float r = v * v; v = vec[1 + offset]; r += v * v; v = vec[2 + offset]; return r + v * v; } /** * Return true if all two vector components are zero, i.e. it's their absolute value < <code>epsilon</code>. * <p> * Implementation uses {@link FloatUtil#isZero(float, float)}, see API doc for details. * </p> */ public static boolean isZero(final float x, final float y, final float epsilon) { return FloatUtil.isZero(x, epsilon) && FloatUtil.isZero(y, epsilon); } /** * Return true if all three vector components are zero, i.e. it's their absolute value < <code>epsilon</code>. * <p> * Implementation uses {@link FloatUtil#isZero(float, float)}, see API doc for details. * </p> */ public static boolean isZero(final float x, final float y, final float z, final float epsilon) { return FloatUtil.isZero(x, epsilon) && FloatUtil.isZero(y, epsilon) && FloatUtil.isZero(z, epsilon); } }