/** * 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. */ package com.jogamp.graph.math; import java.util.ArrayList; import jogamp.graph.math.MathFloat; import com.jogamp.graph.geom.Vertex; public class VectorUtil { public enum Winding { CW(-1), CCW(1); public final int dir; Winding(int dir) { this.dir = dir; } } public static final int COLLINEAR = 0; /** compute the dot product of two points * @param vec1 vector 1 * @param vec2 vector 2 * @return the dot product as float */ public static float dot(float[] vec1, float[] vec2) { return (vec1[0]*vec2[0] + vec1[1]*vec2[1] + vec1[2]*vec2[2]); } /** Normalize a vector * @param vector input vector * @return normalized vector */ public static float[] normalize(float[] vector) { float[] newVector = new float[3]; float d = MathFloat.sqrt(vector[0]*vector[0] + vector[1]*vector[1] + vector[2]*vector[2]); if(d> 0.0f) { newVector[0] = vector[0]/d; newVector[1] = vector[1]/d; newVector[2] = vector[2]/d; } return newVector; } /** Scales a vector by param * @param vector input vector * @param scale constant to scale by * @return scaled vector */ public static float[] scale(float[] vector, float scale) { float[] newVector = new float[3]; newVector[0] = vector[0]*scale; newVector[1] = vector[1]*scale; newVector[2] = vector[2]*scale; return newVector; } /** Adds to vectors * @param v1 vector 1 * @param v2 vector 2 * @return v1 + v2 */ public static float[] vectorAdd(float[] v1, float[] v2) { float[] newVector = new float[3]; newVector[0] = v1[0] + v2[0]; newVector[1] = v1[1] + v2[1]; newVector[2] = v1[2] + v2[2]; return newVector; } /** cross product vec1 x vec2 * @param vec1 vector 1 * @param vec2 vecttor 2 * @return the resulting vector */ public static float[] cross(float[] vec1, float[] vec2) { float[] out = new float[3]; out[0] = vec2[2]*vec1[1] - vec2[1]*vec1[2]; out[1] = vec2[0]*vec1[2] - vec2[2]*vec1[0]; out[2] = vec2[1]*vec1[0] - vec2[0]*vec1[1]; return out; } /** Column Matrix Vector multiplication * @param colMatrix column matrix (4x4) * @param vec vector(x,y,z) * @return result new float[3] */ public static float[] colMatrixVectorMult(float[] colMatrix, float[] vec) { float[] out = new float[3]; out[0] = vec[0]*colMatrix[0] + vec[1]*colMatrix[4] + vec[2]*colMatrix[8] + colMatrix[12]; out[1] = vec[0]*colMatrix[1] + vec[1]*colMatrix[5] + vec[2]*colMatrix[9] + colMatrix[13]; out[2] = vec[0]*colMatrix[2] + vec[1]*colMatrix[6] + vec[2]*colMatrix[10] + colMatrix[14]; return out; } /** Matrix Vector multiplication * @param rawMatrix column matrix (4x4) * @param vec vector(x,y,z) * @return result new float[3] */ public static float[] rowMatrixVectorMult(float[] rawMatrix, float[] vec) { float[] out = new float[3]; out[0] = vec[0]*rawMatrix[0] + vec[1]*rawMatrix[1] + vec[2]*rawMatrix[2] + rawMatrix[3]; out[1] = vec[0]*rawMatrix[4] + vec[1]*rawMatrix[5] + vec[2]*rawMatrix[6] + rawMatrix[7]; out[2] = vec[0]*rawMatrix[8] + vec[1]*rawMatrix[9] + vec[2]*rawMatrix[10] + rawMatrix[11]; return out; } /** Calculate the midpoint of two values * @param p1 first value * @param p2 second vale * @return midpoint */ public static float mid(float p1, float p2) { return (p1+p2)/2.0f; } /** Calculate the midpoint of two points * @param p1 first point * @param p2 second point * @return midpoint */ public static float[] mid(float[] p1, float[] p2) { float[] midPoint = new float[3]; midPoint[0] = (p1[0] + p2[0])*0.5f; midPoint[1] = (p1[1] + p2[1])*0.5f; midPoint[2] = (p1[2] + p2[2])*0.5f; return midPoint; } /** Compute the norm of a vector * @param vec vector * @return vorm */ public static float norm(float[] vec) { return MathFloat.sqrt(vec[0]*vec[0] + vec[1]*vec[1] + vec[2]*vec[2]); } /** Compute distance between 2 points * @param p0 a ref point on the line * @param vec vector representing the direction of the line * @param point the point to compute the relative distance of * @return distance float */ public static float computeLength(float[] p0, float[] point) { float[] w = new float[]{point[0]-p0[0],point[1]-p0[1],point[2]-p0[2]}; float distance = MathFloat.sqrt(w[0]*w[0] + w[1]*w[1] + w[2]*w[2]); return distance; } /**Check equality of 2 vec3 vectors * @param v1 vertex 1 * @param v2 vertex 2 * @return */ public static boolean checkEquality(float[] v1, float[] v2) { if(Float.compare(v1[0], v2[0]) == 0 && Float.compare(v1[1], v2[1]) == 0 && Float.compare(v1[2], v2[2]) == 0 ) return true; return false; } /**Check equality of 2 vec2 vectors * @param v1 vertex 1 * @param v2 vertex 2 * @return */ public static boolean checkEqualityVec2(float[] v1, float[] v2) { if(Float.compare(v1[0], v2[0]) == 0 && Float.compare(v1[1], v2[1]) == 0) return true; return false; } /** Compute the determinant of 3 vectors * @param a vector 1 * @param b vector 2 * @param c vector 3 * @return the determinant value */ public static float computeDeterminant(float[] a, float[] b, float[] c) { float area = a[0]*b[1]*c[2] + a[1]*b[2]*c[0] + a[2]*b[0]*c[1] - a[0]*b[2]*c[1] - a[1]*b[0]*c[2] - a[2]*b[1]*c[0]; return area; } /** Check if three vertices are colliniear * @param v1 vertex 1 * @param v2 vertex 2 * @param v3 vertex 3 * @return true if collinear, false otherwise */ public static boolean checkCollinear(float[] v1, float[] v2, float[] v3) { return (computeDeterminant(v1, v2, v3) == VectorUtil.COLLINEAR); } /** Compute Vector * @param v1 vertex 1 * @param v2 vertex2 2 * @return Vector V1V2 */ public static float[] computeVector(float[] v1, float[] v2) { float[] vector = new float[3]; vector[0] = v2[0] - v1[0]; vector[1] = v2[1] - v1[1]; vector[2] = v2[2] - v1[2]; return vector; } /** Check if vertices in triangle circumcircle * @param a triangle vertex 1 * @param b triangle vertex 2 * @param c triangle vertex 3 * @param d vertex in question * @return true if the vertex d is inside the circle defined by the * vertices a, b, c. from paper by Guibas and Stolfi (1985). */ public static boolean inCircle(Vertex a, Vertex b, Vertex c, Vertex d){ return (a.getX() * a.getX() + a.getY() * a.getY()) * triArea(b, c, d) - (b.getX() * b.getX() + b.getY() * b.getY()) * triArea(a, c, d) + (c.getX() * c.getX() + c.getY() * c.getY()) * triArea(a, b, d) - (d.getX() * d.getX() + d.getY() * d.getY()) * triArea(a, b, c) > 0; } /** Computes oriented area of a triangle * @param a first vertex * @param b second vertex * @param c third vertex * @return compute twice the area of the oriented triangle (a,b,c), the area * is positive if the triangle is oriented counterclockwise. */ public static float triArea(Vertex a, Vertex b, Vertex c){ return (b.getX() - a.getX()) * (c.getY() - a.getY()) - (b.getY() - a.getY())*(c.getX() - a.getX()); } /** Check if a vertex is in triangle using * barycentric coordinates computation. * @param a first triangle vertex * @param b second triangle vertex * @param c third triangle vertex * @param p the vertex in question * @return true if p is in triangle (a, b, c), false otherwise. */ public static boolean vertexInTriangle(float[] a, float[] b, float[] c, float[] p){ // Compute vectors float[] ac = computeVector(a, c); //v0 float[] ab = computeVector(a, b); //v1 float[] ap = computeVector(a, p); //v2 // Compute dot products float dot00 = dot(ac, ac); float dot01 = dot(ac, ab); float dot02 = dot(ac, ap); float dot11 = dot(ab, ab); float dot12 = dot(ab, ap); // Compute barycentric coordinates float invDenom = 1 / (dot00 * dot11 - dot01 * dot01); float u = (dot11 * dot02 - dot01 * dot12) * invDenom; float v = (dot00 * dot12 - dot01 * dot02) * invDenom; // Check if point is in triangle return (u >= 0) && (v >= 0) && (u + v < 1); } /** Check if points are in ccw order * @param a first vertex * @param b second vertex * @param c third vertex * @return true if the points a,b,c are in a ccw order */ public static boolean ccw(Vertex a, Vertex b, Vertex c){ return triArea(a,b,c) > 0; } /** Compute the winding of given points * @param a first vertex * @param b second vertex * @param c third vertex * @return Winding */ public static Winding getWinding(Vertex a, Vertex b, Vertex c) { return triArea(a,b,c) > 0 ? Winding.CCW : Winding.CW ; } /** Computes the area of a list of vertices to check if ccw * @param vertices * @return positive area if ccw else negative area value */ public static float area(ArrayList vertices) { int n = vertices.size(); float area = 0.0f; for (int p = n - 1, q = 0; q < n; p = q++) { float[] pCoord = vertices.get(p).getCoord(); float[] qCoord = vertices.get(q).getCoord(); area += pCoord[0] * qCoord[1] - qCoord[0] * pCoord[1]; } return area; } /** Compute the general winding of the vertices * @param vertices array of Vertices * @return CCW or CW {@link Winding} */ public static Winding getWinding(ArrayList vertices) { return area(vertices) >= 0 ? Winding.CCW : Winding.CW ; } /** Compute intersection between two segments * @param a vertex 1 of first segment * @param b vertex 2 of first segment * @param c vertex 1 of second segment * @param d vertex 2 of second segment * @return the intersection coordinates if the segments intersect, otherwise * returns null */ public static float[] seg2SegIntersection(Vertex a, Vertex b, Vertex c, Vertex d) { float determinant = (a.getX()-b.getX())*(c.getY()-d.getY()) - (a.getY()-b.getY())*(c.getX()-d.getX()); if (determinant == 0) return null; float alpha = (a.getX()*b.getY()-a.getY()*b.getX()); float beta = (c.getX()*d.getY()-c.getY()*d.getY()); float xi = ((c.getX()-d.getX())*alpha-(a.getX()-b.getX())*beta)/determinant; float yi = ((c.getY()-d.getY())*alpha-(a.getY()-b.getY())*beta)/determinant; float gamma = (xi - a.getX())/(b.getX() - a.getX()); float gamma1 = (xi - c.getX())/(d.getX() - c.getX()); if(gamma <= 0 || gamma >= 1) return null; if(gamma1 <= 0 || gamma1 >= 1) return null; return new float[]{xi,yi,0}; } /** Compute intersection between two lines * @param a vertex 1 of first line * @param b vertex 2 of first line * @param c vertex 1 of second line * @param d vertex 2 of second line * @return the intersection coordinates if the lines intersect, otherwise * returns null */ public static float[] line2lineIntersection(Vertex a, Vertex b, Vertex c, Vertex d) { float determinant = (a.getX()-b.getX())*(c.getY()-d.getY()) - (a.getY()-b.getY())*(c.getX()-d.getX()); if (determinant == 0) return null; float alpha = (a.getX()*b.getY()-a.getY()*b.getX()); float beta = (c.getX()*d.getY()-c.getY()*d.getY()); float xi = ((c.getX()-d.getX())*alpha-(a.getX()-b.getX())*beta)/determinant; float yi = ((c.getY()-d.getY())*alpha-(a.getY()-b.getY())*beta)/determinant; return new float[]{xi,yi,0}; } /** Check if a segment intersects with a triangle * @param a vertex 1 of the triangle * @param b vertex 2 of the triangle * @param c vertex 3 of the triangle * @param d vertex 1 of first segment * @param e vertex 2 of first segment * @return true if the segment intersects at least one segment of the triangle, false otherwise */ public static boolean tri2SegIntersection(Vertex a, Vertex b, Vertex c, Vertex d, Vertex e){ if(seg2SegIntersection(a, b, d, e) != null) return true; if(seg2SegIntersection(b, c, d, e) != null) return true; if(seg2SegIntersection(a, c, d, e) != null) return true; return false; } }