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-/**
- * Copyright 2010-2023 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.opengl.math;
-
-import java.util.ArrayList;
-
-import com.jogamp.graph.geom.plane.Winding;
-
-public final class VectorUtil {
- /**
- * Return true if 2D vector components are zero, no {@link FloatUtil#EPSILON} is taken into consideration.
- */
- public static boolean isVec2Zero(final Vec3f vec) {
- return 0f == vec.x() && 0f == vec.y();
- }
-
- /**
- * 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) ;
- }
-
- /**
- * Return true if all three vector components are zero, i.e. it's their absolute value < {@link FloatUtil#EPSILON}.
- * <p>
- * Implementation uses {@link FloatUtil#isZero(float)}, see API doc for details.
- * </p>
- */
- public static boolean isZero(final float x, final float y, final float z) {
- return FloatUtil.isZero(x) &&
- FloatUtil.isZero(y) &&
- FloatUtil.isZero(z) ;
- }
-
- /**
- * Return the squared distance between the given two points described vector v1 and v2.
- * <p>
- * When comparing the relative distance between two points it is usually sufficient to compare the squared
- * distances, thus avoiding an expensive square root operation.
- * </p>
- */
- public static float distSquareVec3(final float[] v1, final float[] v2) {
- final float dx = v1[0] - v2[0];
- final float dy = v1[1] - v2[1];
- final float dz = v1[2] - v2[2];
- return dx * dx + dy * dy + dz * dz;
- }
-
- /**
- * Return the distance between the given two points described vector v1 and v2.
- */
- public static float distVec3(final float[] v1, final float[] v2) {
- return FloatUtil.sqrt(distSquareVec3(v1, v2));
- }
-
- /**
- * Return the squared length of a vector, a.k.a the squared <i>norm</i> or squared <i>magnitude</i>
- */
- public static float normSquareVec2(final float[] vec) {
- return vec[0]*vec[0] + vec[1]*vec[1];
- }
-
- /**
- * 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 the length of a vector, a.k.a the <i>norm</i> or <i>magnitude</i>
- */
- public static float normVec2(final float[] vec) {
- return FloatUtil.sqrt(normSquareVec2(vec));
- }
-
- /**
- * 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;
- }
-
- /**
- * Scales a vector by param using given result float[], result = vector * scale
- * @param result vector for the result, may be vector (in-place)
- * @param vector input vector
- * @param scale single scale constant for all vector components
- * @return result vector for chaining
- */
- public static float[] scaleVec2(final float[] result, final float[] vector, final float scale) {
- result[0] = vector[0] * scale;
- result[1] = vector[1] * scale;
- return result;
- }
-
- /**
- * Scales a vector by param using given result float[], result = vector * scale
- * @param result vector for the result, may be vector (in-place)
- * @param vector input vector
- * @param scale 2 component scale constant for each vector component
- * @return result vector for chaining
- */
- public static float[] scaleVec2(final float[] result, final float[] vector, final float[] scale)
- {
- result[0] = vector[0] * scale[0];
- result[1] = vector[1] * scale[1];
- return result;
- }
-
- /**
- * Divides a vector by param using given result float[], result = vector / scale
- * @param result vector for the result, may be vector (in-place)
- * @param vector input vector
- * @param scale single scale constant for all vector components
- * @return result vector for chaining
- */
- public static float[] divVec2(final float[] result, final float[] vector, final float scale) {
- result[0] = vector[0] / scale;
- result[1] = vector[1] / scale;
- return result;
- }
-
- /**
- * Divides a vector by param using given result float[], result = vector / scale
- * @param result vector for the result, may be vector (in-place)
- * @param vector input vector
- * @param scale 2 component scale constant for each vector component
- * @return result vector for chaining
- */
- public static float[] divVec2(final float[] result, final float[] vector, final float[] scale)
- {
- result[0] = vector[0] / scale[0];
- result[1] = vector[1] / scale[1];
- return result;
- }
-
- /**
- * Adds two vectors, result = v1 + v2
- * @param result float[2] 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[] addVec2(final float[] result, final float[] v1, final float[] v2) {
- result[0] = v1[0] + v2[0];
- result[1] = v1[1] + v2[1];
- return result;
- }
-
- /**
- * Subtracts two vectors, result = v1 - v2
- * @param result float[2] 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[] subVec2(final float[] result, final float[] v1, final float[] v2) {
- result[0] = v1[0] - v2[0];
- result[1] = v1[1] - v2[1];
- 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;
- }
-
- /**
- * Calculate the midpoint of two points
- * @param p1 first point vector
- * @param p2 second point vector
- * @return midpoint
- */
- public static Vec3f midVec3(final Vec3f result, final Vec3f p1, final Vec3f p2) {
- result.set( (p1.x() + p2.x())*0.5f,
- (p1.y() + p2.y())*0.5f,
- (p1.z() + p2.z())*0.5f );
- return result;
- }
-
- /**
- * Return the determinant of 3 vectors
- * @param a vector 1
- * @param b vector 2
- * @param c vector 3
- * @return the determinant value
- */
- public static float determinantVec3(final Vec3f a, final Vec3f b, final Vec3f c) {
- return a.x()*b.y()*c.z() + a.y()*b.z()*c.x() + a.z()*b.x()*c.y() - a.x()*b.z()*c.y() - a.y()*b.x()*c.z() - a.z()*b.y()*c.x();
- }
-
- /**
- * 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 isCollinearVec3(final Vec3f v1, final Vec3f v2, final Vec3f v3) {
- return FloatUtil.isZero( determinantVec3(v1, v2, v3), FloatUtil.EPSILON );
- }
-
- /**
- * 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 isInCircleVec2(final Vert2fImmutable a, final Vert2fImmutable b, final Vert2fImmutable c, final Vert2fImmutable d) {
- return (a.x() * a.x() + a.y() * a.y()) * triAreaVec2(b, c, d) -
- (b.x() * b.x() + b.y() * b.y()) * triAreaVec2(a, c, d) +
- (c.x() * c.x() + c.y() * c.y()) * triAreaVec2(a, b, d) -
- (d.x() * d.x() + d.y() * d.y()) * triAreaVec2(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 triAreaVec2(final Vert2fImmutable a, final Vert2fImmutable b, final Vert2fImmutable c){
- return (b.x() - a.x()) * (c.y() - a.y()) - (b.y() - a.y()) * (c.x() - a.x());
- }
-
- /**
- * 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
- * @param ac temporary storage
- * @param ab temporary storage
- * @param ap temporary storage
- * @return true if p is in triangle (a, b, c), false otherwise.
- */
- public static boolean isInTriangleVec3(final Vec3f a, final Vec3f b, final Vec3f c,
- final Vec3f p,
- final Vec3f ac, final Vec3f ab, final Vec3f ap){
- // Compute vectors
- ac.minus( c, a); // v0
- ab.minus( b, a); // v1
- ap.minus( p, a); // v2
-
- // Compute dot products
- final float dotAC_AC = ac.dot(ac);
- final float dotAC_AB = ac.dot(ab);
- final float dotAB_AB = ab.dot(ab);
- final float dotAC_AP = ac.dot(ap);
- final float dotAB_AP = ab.dot(ap);
-
- // Compute barycentric coordinates
- final float invDenom = 1 / (dotAC_AC * dotAB_AB - dotAC_AB * dotAC_AB);
- final float u = (dotAB_AB * dotAC_AP - dotAC_AB * dotAB_AP) * invDenom;
- final float v = (dotAC_AC * dotAB_AP - dotAC_AB * dotAC_AP) * invDenom;
-
- // Check if point is in triangle
- return (u >= 0) && (v >= 0) && (u + v < 1);
- }
-
- /**
- * Check if one of three vertices are in triangle using barycentric coordinates computation.
- * @param a first triangle vertex
- * @param b second triangle vertex
- * @param c third triangle vertex
- * @param p1 the vertex in question
- * @param p2 the vertex in question
- * @param p3 the vertex in question
- * @param ac temporary storage
- * @param ab temporary storage
- * @param ap temporary storage
- * @return true if p1 or p2 or p3 is in triangle (a, b, c), false otherwise.
- */
- public static boolean isVec3InTriangle3(final Vec3f a, final Vec3f b, final Vec3f c,
- final Vec3f p1, final Vec3f p2, final Vec3f p3,
- final Vec3f ac, final Vec3f ab, final Vec3f ap){
- // Compute vectors
- ac.minus(c, a); // v0
- ab.minus(b, a); // v1
-
- // Compute dot products
- final float dotAC_AC = ac.dot(ac);
- final float dotAC_AB = ac.dot(ab);
- final float dotAB_AB = ab.dot(ab);
-
- // Compute barycentric coordinates
- final float invDenom = 1 / (dotAC_AC * dotAB_AB - dotAC_AB * dotAC_AB);
- {
- ap.minus(p1, a); // v2
- final float dotAC_AP1 = ac.dot(ap);
- final float dotAB_AP1 = ab.dot(ap);
- final float u = (dotAB_AB * dotAC_AP1 - dotAC_AB * dotAB_AP1) * invDenom;
- final float v = (dotAC_AC * dotAB_AP1 - dotAC_AB * dotAC_AP1) * invDenom;
-
- // Check if point is in triangle
- if ( (u >= 0) && (v >= 0) && (u + v < 1) ) {
- return true;
- }
- }
-
- {
- ap.minus(p2, a); // v2
- final float dotAC_AP2 = ac.dot(ap);
- final float dotAB_AP2 = ab.dot(ap);
- final float u = (dotAB_AB * dotAC_AP2 - dotAC_AB * dotAB_AP2) * invDenom;
- final float v = (dotAC_AC * dotAB_AP2 - dotAC_AB * dotAC_AP2) * invDenom;
-
- // Check if point is in triangle
- if ( (u >= 0) && (v >= 0) && (u + v < 1) ) {
- return true;
- }
- }
-
- {
- ap.minus(p3, a); // v3
- final float dotAC_AP3 = ac.dot(ap);
- final float dotAB_AP3 = ab.dot(ap);
- final float u = (dotAB_AB * dotAC_AP3 - dotAC_AB * dotAB_AP3) * invDenom;
- final float v = (dotAC_AC * dotAB_AP3 - dotAC_AB * dotAC_AP3) * invDenom;
-
- // Check if point is in triangle
- if ( (u >= 0) && (v >= 0) && (u + v < 1) ) {
- return true;
- }
- }
- return false;
- }
- /**
- * Check if one of three vertices are in triangle using
- * barycentric coordinates computation, using given epsilon for comparison.
- * @param a first triangle vertex
- * @param b second triangle vertex
- * @param c third triangle vertex
- * @param p1 the vertex in question
- * @param p2 the vertex in question
- * @param p3 the vertex in question
- * @param tmpAC
- * @param tmpAB
- * @param tmpAP
- * @return true if p1 or p2 or p3 is in triangle (a, b, c), false otherwise.
- */
- public static boolean isVec3InTriangle3(final Vec3f a, final Vec3f b, final Vec3f c,
- final Vec3f p1, final Vec3f p2, final Vec3f p3,
- final Vec3f ac, final Vec3f ab, final Vec3f ap,
- final float epsilon) {
- // Compute vectors
- ac.minus(c, a); // v0
- ab.minus(b, a); // v1
-
- // Compute dot products
- final float dotAC_AC = ac.dot(ac);
- final float dotAC_AB = ac.dot(ab);
- final float dotAB_AB = ab.dot(ab);
-
- // Compute barycentric coordinates
- final float invDenom = 1 / (dotAC_AC * dotAB_AB - dotAC_AB * dotAC_AB);
- {
- ap.minus(p1, a); // v2
- final float dotAC_AP1 = ac.dot(ap);
- final float dotAB_AP1 = ab.dot(ap);
- final float u = (dotAB_AB * dotAC_AP1 - dotAC_AB * dotAB_AP1) * invDenom;
- final float v = (dotAC_AC * dotAB_AP1 - dotAC_AB * dotAC_AP1) * invDenom;
-
- // Check if point is in triangle
- if( FloatUtil.compare(u, 0.0f, epsilon) >= 0 &&
- FloatUtil.compare(v, 0.0f, epsilon) >= 0 &&
- FloatUtil.compare(u+v, 1.0f, epsilon) < 0 ) {
- return true;
- }
- }
-
- {
- ap.minus(p2, a); // v3
- final float dotAC_AP2 = ac.dot(ap);
- final float dotAB_AP2 = ab.dot(ap);
- final float u = (dotAB_AB * dotAC_AP2 - dotAC_AB * dotAB_AP2) * invDenom;
- final float v = (dotAC_AC * dotAB_AP2 - dotAC_AB * dotAC_AP2) * invDenom;
-
- // Check if point is in triangle
- if( FloatUtil.compare(u, 0.0f, epsilon) >= 0 &&
- FloatUtil.compare(v, 0.0f, epsilon) >= 0 &&
- FloatUtil.compare(u+v, 1.0f, epsilon) < 0 ) {
- return true;
- }
- }
-
- {
- ap.minus(p3, a); // v4
- final float dotAC_AP3 = ac.dot(ap);
- final float dotAB_AP3 = ab.dot(ap);
- final float u = (dotAB_AB * dotAC_AP3 - dotAC_AB * dotAB_AP3) * invDenom;
- final float v = (dotAC_AC * dotAB_AP3 - dotAC_AB * dotAC_AP3) * invDenom;
-
- // Check if point is in triangle
- if( FloatUtil.compare(u, 0.0f, epsilon) >= 0 &&
- FloatUtil.compare(v, 0.0f, epsilon) >= 0 &&
- FloatUtil.compare(u+v, 1.0f, epsilon) < 0 ) {
- return true;
- }
- }
- return false;
- }
-
- /**
- * 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 isCCW(final Vert2fImmutable a, final Vert2fImmutable b, final Vert2fImmutable c){
- return triAreaVec2(a,b,c) > 0;
- }
-
- /**
- * Compute the winding of the 3 given points
- * <p>
- * Consider using {@link #getWinding(ArrayList)} using the {@link #area(ArrayList)} function over all points
- * on complex shapes for a reliable result!
- * </p>
- * @param a first vertex
- * @param b second vertex
- * @param c third vertex
- * @return {@link Winding#CCW} or {@link Winding#CW}
- * @see #getWinding(ArrayList)
- */
- public static Winding getWinding(final Vert2fImmutable a, final Vert2fImmutable b, final Vert2fImmutable c) {
- return triAreaVec2(a,b,c) > 0 ? Winding.CCW : Winding.CW ;
- }
-
- /**
- * Computes the area of a list of vertices.
- * <p>
- * This method is utilized e.g. to reliably compute the {@link Winding} of complex shapes.
- * </p>
- * @param vertices
- * @return positive area if ccw else negative area value
- * @see #getWinding(ArrayList)
- */
- public static float area(final ArrayList<? extends Vert2fImmutable> vertices) {
- final int n = vertices.size();
- float area = 0.0f;
- for (int p = n - 1, q = 0; q < n; p = q++) {
- final Vert2fImmutable pCoord = vertices.get(p);
- final Vert2fImmutable qCoord = vertices.get(q);
- area += pCoord.x() * qCoord.y() - qCoord.x() * pCoord.y();
- }
- return area;
- }
-
- /**
- * Compute the winding using the {@link #area(ArrayList)} function over all vertices for complex shapes.
- * <p>
- * Uses the {@link #area(ArrayList)} function over all points
- * on complex shapes for a reliable result!
- * </p>
- * @param vertices array of Vertices
- * @return {@link Winding#CCW} or {@link Winding#CW}
- * @see #area(ArrayList)
- */
- public static Winding getWinding(final ArrayList<? extends Vert2fImmutable> vertices) {
- return area(vertices) >= 0 ? Winding.CCW : Winding.CW ;
- }
-
- /**
- * 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 Vec4f getPlaneVec3(final Vec4f resultV4, final Vec3f normalVec3, final Vec3f pVec3) {
- /**
- Ax + By + Cz + D == 0 ;
- D = - ( Ax + By + Cz )
- = - ( A*a[0] + B*a[1] + C*a[2] )
- = - vec3Dot ( normal, a ) ;
- */
- resultV4.set(normalVec3, -normalVec3.dot(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 Vec4f getPlaneVec3(final Vec4f resultVec4, final Vec3f v1, final Vec3f v2, final Vec3f v3,
- final Vec3f temp1V3, final Vec3f temp2V3, final Vec3f temp3V3) {
- /**
- Ax + By + Cz + D == 0 ;
- D = - ( Ax + By + Cz )
- = - ( A*a[0] + B*a[1] + C*a[2] )
- = - vec3Dot ( normal, a ) ;
- */
- temp3V3.cross(temp1V3.minus(v2, v1), temp2V3.minus(v3, v1)).normalize();
- resultVec4.set(temp3V3, -temp3V3.dot(v1));
- return resultVec4;
- }
-
- /**
- * Return intersection of an infinite line with a plane if exists, otherwise null.
- * <p>
- * Thanks to <i>Norman Vine -- [email protected] (with hacks by Steve)</i>
- * </p>
- *
- * @param result vec3 result buffer for intersecting coords
- * @param ray here representing an infinite line, origin and direction.
- * @param plane vec4 plane equation
- * @param epsilon
- * @return resulting intersecting if exists, otherwise null
- */
- public static Vec3f line2PlaneIntersection(final Vec3f result, final Ray ray, final Vec4f plane, final float epsilon) {
- final Vec3f plane3 = new Vec3f(plane);
- final float tmp = ray.dir.dot(plane3);
-
- if ( Math.abs(tmp) < epsilon ) {
- return null; // ray is parallel to plane
- }
- result.set( ray.dir );
- return result.scale( -( ray.orig.dot(plane3) + plane.w() ) / tmp ).add(ray.orig);
- }
-
- /** 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 Vec3f seg2SegIntersection(final Vec3f result, final Vert2fImmutable a, final Vert2fImmutable b, final Vert2fImmutable c, final Vert2fImmutable d) {
- final float determinant = (a.x()-b.x())*(c.y()-d.y()) - (a.y()-b.y())*(c.x()-d.x());
-
- if (determinant == 0)
- return null;
-
- final float alpha = (a.x()*b.y()-a.y()*b.x());
- final float beta = (c.x()*d.y()-c.y()*d.y());
- final float xi = ((c.x()-d.x())*alpha-(a.x()-b.x())*beta)/determinant;
- final float yi = ((c.y()-d.y())*alpha-(a.y()-b.y())*beta)/determinant;
-
- final float gamma = (xi - a.x())/(b.x() - a.x());
- final float gamma1 = (xi - c.x())/(d.x() - c.x());
- if(gamma <= 0 || gamma >= 1) return null;
- if(gamma1 <= 0 || gamma1 >= 1) return null;
-
- return result.set(xi, yi, 0);
- }
-
- /**
- * 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 true if the segments intersect, otherwise returns false
- */
- public static boolean testSeg2SegIntersection(final Vert2fImmutable a, final Vert2fImmutable b,
- final Vert2fImmutable c, final Vert2fImmutable d) {
- final float determinant = (a.x()-b.x())*(c.y()-d.y()) - (a.y()-b.y())*(c.x()-d.x());
-
- if (determinant == 0) {
- return false;
- }
-
- final float alpha = (a.x()*b.y()-a.y()*b.x());
- final float beta = (c.x()*d.y()-c.y()*d.y());
- final float xi = ((c.x()-d.x())*alpha-(a.x()-b.x())*beta)/determinant;
-
- final float gamma0 = (xi - a.x())/(b.x() - a.x());
- final float gamma1 = (xi - c.x())/(d.x() - c.x());
- if(gamma0 <= 0 || gamma0 >= 1 || gamma1 <= 0 || gamma1 >= 1) {
- return false;
- }
-
- return true;
- }
- /**
- * Compute intersection between two segments, using given epsilon for comparison.
- * @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 true if the segments intersect, otherwise returns false
- */
- public static boolean testSeg2SegIntersection(final Vert2fImmutable a, final Vert2fImmutable b,
- final Vert2fImmutable c, final Vert2fImmutable d,
- final float epsilon) {
- final float determinant = (a.x()-b.x())*(c.y()-d.y()) - (a.y()-b.y())*(c.x()-d.x());
-
- if ( FloatUtil.isZero(determinant, epsilon) ) {
- return false;
- }
-
- final float alpha = (a.x()*b.y()-a.y()*b.x());
- final float beta = (c.x()*d.y()-c.y()*d.y());
- final float xi = ((c.x()-d.x())*alpha-(a.x()-b.x())*beta)/determinant;
-
- final float gamma0 = (xi - a.x())/(b.x() - a.x());
- final float gamma1 = (xi - c.x())/(d.x() - c.x());
-
- if( FloatUtil.compare(gamma0, 0.0f, epsilon) <= 0 ||
- FloatUtil.compare(gamma0, 1.0f, epsilon) >= 0 ||
- FloatUtil.compare(gamma1, 0.0f, epsilon) <= 0 ||
- FloatUtil.compare(gamma1, 1.0f, epsilon) >= 0 ) {
- return false;
- }
-
- if(gamma0 <= 0 || gamma0 >= 1 || gamma1 <= 0 || gamma1 >= 1) {
- return false;
- }
-
- return true;
- }
-
- /**
- * 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 Vec3f line2lineIntersection(final Vec3f result,
- final Vert2fImmutable a, final Vert2fImmutable b,
- final Vert2fImmutable c, final Vert2fImmutable d) {
- final float determinant = (a.x()-b.x())*(c.y()-d.y()) - (a.y()-b.y())*(c.x()-d.x());
-
- if (determinant == 0)
- return null;
-
- final float alpha = (a.x()*b.y()-a.y()*b.x());
- final float beta = (c.x()*d.y()-c.y()*d.y());
- final float xi = ((c.x()-d.x())*alpha-(a.x()-b.x())*beta)/determinant;
- final float yi = ((c.y()-d.y())*alpha-(a.y()-b.y())*beta)/determinant;
-
- return result.set(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 testTri2SegIntersection(final Vert2fImmutable a, final Vert2fImmutable b, final Vert2fImmutable c,
- final Vert2fImmutable d, final Vert2fImmutable e){
- return testSeg2SegIntersection(a, b, d, e) ||
- testSeg2SegIntersection(b, c, d, e) ||
- testSeg2SegIntersection(a, c, d, e) ;
- }
- /**
- * Check if a segment intersects with a triangle, using given epsilon for comparison.
- * @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 testTri2SegIntersection(final Vert2fImmutable a, final Vert2fImmutable b, final Vert2fImmutable c,
- final Vert2fImmutable d, final Vert2fImmutable e,
- final float epsilon){
- return testSeg2SegIntersection(a, b, d, e, epsilon) ||
- testSeg2SegIntersection(b, c, d, e, epsilon) ||
- testSeg2SegIntersection(a, c, d, e, epsilon) ;
- }
-}
generated by cgit v1.2.3 (git 2.39.1) at 2025-03-19 16:22:38 +0000