Java tutorial
/* GeoGebra - Dynamic Mathematics for Everyone http://www.geogebra.org This file is part of GeoGebra. This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation. */ /* * GeoVec2D.java * * Created on 31. August 2001, 11:34 */ package org.geogebra.common.geogebra3D.kernel3D.geos; import java.util.HashSet; import org.apache.commons.math.complex.Complex; import org.geogebra.common.kernel.Kernel; import org.geogebra.common.kernel.StringTemplate; import org.geogebra.common.kernel.Matrix.Coords; import org.geogebra.common.kernel.arithmetic.ExpressionNode; import org.geogebra.common.kernel.arithmetic.ExpressionValue; import org.geogebra.common.kernel.arithmetic.MyDouble; import org.geogebra.common.kernel.arithmetic.MyList; import org.geogebra.common.kernel.arithmetic.ValidExpression; import org.geogebra.common.kernel.arithmetic.VectorNDValue; import org.geogebra.common.kernel.arithmetic3D.Vector3DValue; import org.geogebra.common.kernel.geos.GeoElement; import org.geogebra.common.kernel.geos.GeoVec2D; import org.geogebra.common.kernel.geos.GeoVec3D; import org.geogebra.common.kernel.kernelND.GeoPointND; import org.geogebra.common.kernel.kernelND.GeoVecInterface; /** * * @author Michael adapted from GeoVec2D * @version */ final public class Geo3DVec extends ValidExpression implements Vector3DValue, org.geogebra.common.kernel.kernelND.Geo3DVec { public double x = Double.NaN; public double y = Double.NaN; public double z = Double.NaN; private int mode = Kernel.COORD_CARTESIAN_3D; private Kernel kernel; /** Creates new GeoVec2D */ public Geo3DVec(Kernel kernel) { this.kernel = kernel; } /** Creates new GeoVec3D with coordinates (x,y) */ public Geo3DVec(Kernel kernel, double x, double y, double z) { this(kernel); this.x = x; this.y = y; this.z = z; } /** Copy constructor */ public Geo3DVec(Geo3DVec v) { this(v.kernel); x = v.x; y = v.y; z = v.z; mode = v.mode; } public ExpressionValue deepCopy(Kernel kernel1) { return new Geo3DVec(this); } public void resolveVariables() { // no variables ? } /** Creates new GeoVec3D as vector between Points P and Q */ public Geo3DVec(Kernel kernel, GeoPoint3D p, GeoPoint3D q) { this(kernel); x = q.getX() - p.getX(); y = q.getY() - p.getY(); z = q.getZ() - p.getZ(); } public void setX(double x) { this.x = x; } public void setY(double y) { this.y = y; } public void setZ(double z) { this.z = z; } public void setCoords(double x, double y, double z) { this.x = x; this.y = y; this.z = z; } public void setCoords(double[] a) { x = a[0]; y = a[1]; z = a[2]; } public void setCoords(GeoVec3D v) { x = v.x; y = v.y; z = v.z; } final public double getX() { return x; } final public double getY() { return y; } final public double getZ() { return z; } // final public double getR() { return length(x, y); } // final public double getPhi() { return Math.atan2(y, x); } final public double[] getCoords() { double[] res = { x, y, z }; return res; } /** * Calculates the eucilidian length of this 2D vector. The result is * sqrt(x^2 + y^2). */ final public double length() { return length(x, y, z); } /** * Calculates the eucilidian length of this 2D vector. The result is * sqrt(a[0]^2 + a[1]^2). */ final public static double length(double[] a) { return length(a[0], a[1], a[2]); } /** * Calculates the euclidian length sqrt(a^2 + b^2). */ final public static double length(double a, double b, double c) { return Math.sqrt(a * a + b * b + c * c); } /** * Changes this vector to a vector with the same direction and orientation, * but length 1. */ final public void makeUnitVector() { double len = this.length(); x = x / len; y = y / len; } /** * Yields true if the coordinates of this vector are equal to those of * vector v. */ final public boolean equals(GeoVec2D v) { return Kernel.isEqual(x, v.getX()) && Kernel.isEqual(y, v.getY()); } /** * Yields true if this vector and v are linear dependent This is done by * calculating the determinant of this vector an v: this = v <=> det(this, * v) = nullvector. */ // final public boolean linDep(GeoVec2D v) { // // v = l* w <=> det(v, w) = o // return kernel.isZero(det(this, v)); // } /** * calculates the determinant of u and v. det(u,v) = u1*v2 - u2*v1 */ /** returns this + a */ // /final public GeoVec2D add(GeoVec2D a) { // / GeoVec2D res = new GeoVec2D(kernel, 0,0); // add(this, a, res); // return res; // } /** c = a + b */ final public static void add(Geo3DVec a, Geo3DVec b, Geo3DVec c) { c.x = a.x + b.x; c.y = a.y + b.y; c.z = a.z + b.z; } /** c = a + b */ final public static void add(Geo3DVec a, GeoVec2D b, Geo3DVec c) { c.x = a.x + b.getX(); c.y = a.y + b.getY(); c.z = a.z; } /** c = a + b */ final public static void add(GeoVec2D a, Geo3DVec b, Geo3DVec c) { c.x = a.getX() + b.x; c.y = a.getY() + b.y; c.z = b.z; } /** c = Vector (Cross) Product of a and b */ final public static void vectorProduct(GeoVecInterface a, GeoVecInterface b, Geo3DVec c) { // tempX/Y needed because a and c can be the same variable double tempX = a.getY() * b.getZ() - a.getZ() * b.getY(); double tempY = -a.getX() * b.getZ() + a.getZ() * b.getX(); c.z = a.getX() * b.getY() - a.getY() * b.getX(); c.x = tempX; c.y = tempY; } /** returns this - a */ // final public GeoVec2D sub(GeoVec2D a) { // GeoVec2D res = new GeoVec2D(kernel, 0,0); // sub(this, a, res); // return res; // } /** c = a - b */ final public static void sub(Geo3DVec a, Geo3DVec b, Geo3DVec c) { c.x = a.x - b.x; c.y = a.y - b.y; c.z = a.z - b.z; } /** c = a - b */ final public static void sub(Geo3DVec a, GeoVec2D b, Geo3DVec c) { c.x = a.x - b.getX(); c.y = a.y - b.getY(); c.z = a.z; } /** c = a - b */ final public static void sub(GeoVec2D a, Geo3DVec b, Geo3DVec c) { c.x = a.getX() - b.x; c.y = a.getY() - b.y; c.z = -b.z; } /** c = a * b */ final public static void mult(Geo3DVec a, double b, Geo3DVec c) { c.x = a.x * b; c.y = a.y * b; c.z = a.z * b; } final public static void inner(GeoVecInterface a, GeoVecInterface b, MyDouble c) { c.set(a.getX() * b.getX() + a.getY() * b.getY() + a.getZ() * b.getZ()); } final public static void complexMultiply(GeoVecInterface a, GeoVecInterface b, GeoVec2D c) { if (!Kernel.isZero(a.getZ()) || !Kernel.isZero(b.getZ())) { c.setX(Double.NaN); c.setY(Double.NaN); c.setMode(Kernel.COORD_COMPLEX); return; } Complex out = new Complex(a.getX(), a.getY()); out = out.multiply(new Complex(b.getX(), b.getY())); c.setX(out.getReal()); c.setY(out.getImaginary()); c.setMode(Kernel.COORD_COMPLEX); } /** c = a / b */ final public static void div(Geo3DVec a, double b, Geo3DVec c) { c.x = a.x / b; c.y = a.y / b; c.z = a.z / b; } @Override final public String toString(StringTemplate tpl) { sbToString.setLength(0); sbToString.append('('); sbToString.append(kernel.format(x, tpl)); sbToString.append(", "); sbToString.append(kernel.format(y, tpl)); sbToString.append(')'); return sbToString.toString(); } private StringBuilder sbToString = new StringBuilder(50); /** * interface VectorValue implementation */ final public Geo3DVec getVector() { return this; } final public boolean isConstant() { return true; } final public boolean isLeaf() { return true; } final public HashSet<GeoElement> getVariables() { return null; } @Override final public String toValueString(StringTemplate tpl) { return toString(tpl); } public String toLaTeXString(boolean symbolic, StringTemplate tpl) { return toString(tpl); } final public boolean isNumberValue() { return false; } final public boolean contains(ExpressionValue ev) { return ev == this; } @Override public boolean evaluatesTo3DVector() { return true; } public double[] getPointAsDouble() { return new double[] { getX(), getY(), getZ() }; } public String toOutputValueString(StringTemplate tpl) { return toValueString(tpl); } public Kernel getKernel() { return kernel; } public boolean isEqual(org.geogebra.common.kernel.kernelND.Geo3DVec vec) { Geo3DVec v = (Geo3DVec) vec; return Kernel.isEqual(x, v.x) && Kernel.isEqual(y, v.y) && Kernel.isEqual(z, v.z); } /** * multiplies 3D vector/point by a 3x3 matrix a b c d e f g h i * * @param list * 3x3 matrix * @param rt * VectorNDValue (as ExpressionValue) to get coords from */ public void multiplyMatrix3x3(MyList list, VectorNDValue rt) { double a, b, c, d, e, f, g, h, i, xx, yy, zz; GeoVecInterface v = rt.getVector(); xx = v.getX(); yy = v.getY(); zz = v.getZ(); a = MyList.getCell(list, 0, 0).evaluateDouble(); b = MyList.getCell(list, 1, 0).evaluateDouble(); c = MyList.getCell(list, 2, 0).evaluateDouble(); d = MyList.getCell(list, 0, 1).evaluateDouble(); e = MyList.getCell(list, 1, 1).evaluateDouble(); f = MyList.getCell(list, 2, 1).evaluateDouble(); g = MyList.getCell(list, 0, 2).evaluateDouble(); h = MyList.getCell(list, 1, 2).evaluateDouble(); i = MyList.getCell(list, 2, 2).evaluateDouble(); x = a * xx + b * yy + c * zz; y = d * xx + e * yy + f * zz; z = g * xx + h * yy + i * zz; return; } /** * multiplies 3D vector/point by a 4x4 matrix a b c d e f g h i * * @param list * 4x4 matrix * @param rt * VectorNDValue (as ExpressionValue) to get coords from */ public void multiplyMatrix4x4(MyList list, VectorNDValue rt) { double m, n, o, p, xx, yy, zz, ww; boolean vector = false; if (rt instanceof GeoPointND) { // 3D point GeoPointND point = (GeoPointND) rt; // use homogeneous coordinates Coords coords = point.getCoordsInD3(); xx = coords.getX(); yy = coords.getY(); zz = coords.getZ(); ww = coords.getW(); } else { GeoVecInterface v = rt.getVector(); xx = v.getX(); yy = v.getY(); zz = v.getZ(); ww = 0; vector = true; } m = MyList.getCell(list, 0, 3).evaluateDouble(); n = MyList.getCell(list, 1, 3).evaluateDouble(); o = MyList.getCell(list, 2, 3).evaluateDouble(); p = MyList.getCell(list, 3, 3).evaluateDouble(); double w = m * xx + n * yy + o * zz + p * ww; if (vector && !Kernel.isZero(w)) { x = Double.NaN; y = Double.NaN; z = Double.NaN; return; } double a, b, c, d, e, f, g, h, i, j, k, l; a = MyList.getCell(list, 0, 0).evaluateDouble(); b = MyList.getCell(list, 1, 0).evaluateDouble(); c = MyList.getCell(list, 2, 0).evaluateDouble(); d = MyList.getCell(list, 3, 0).evaluateDouble(); e = MyList.getCell(list, 0, 1).evaluateDouble(); f = MyList.getCell(list, 1, 1).evaluateDouble(); g = MyList.getCell(list, 2, 1).evaluateDouble(); h = MyList.getCell(list, 3, 1).evaluateDouble(); i = MyList.getCell(list, 0, 2).evaluateDouble(); j = MyList.getCell(list, 1, 2).evaluateDouble(); k = MyList.getCell(list, 2, 2).evaluateDouble(); l = MyList.getCell(list, 3, 2).evaluateDouble(); x = a * xx + b * yy + c * zz + d * ww; y = e * xx + f * yy + g * zz + h * ww; z = i * xx + j * yy + k * zz + l * ww; if (!vector) { x = x / w; y = y / w; z = z / w; } } /** * multiplies 3D vector/point by a 2x3 matrix a b d e g h * * @param list * 2x3 matrix * @param rt * VectorNDValue (as ExpressionValue) to get coords from */ public void multiplyMatrix3x2(MyList list, VectorNDValue rt) { double a, b, d, e, g, h, xx, yy; GeoVecInterface v = rt.getVector(); xx = v.getX(); yy = v.getY(); a = MyList.getCell(list, 0, 0).evaluateDouble(); b = MyList.getCell(list, 1, 0).evaluateDouble(); d = MyList.getCell(list, 0, 1).evaluateDouble(); e = MyList.getCell(list, 1, 1).evaluateDouble(); g = MyList.getCell(list, 0, 2).evaluateDouble(); h = MyList.getCell(list, 1, 2).evaluateDouble(); x = a * xx + b * yy; y = d * xx + e * yy; z = g * xx + h * yy; return; } /** * multiplies 3D vector/point by a 2x3 matrix a b c d e f * * @param list * 2x3 matrix * @param rt * VectorNDValue (as ExpressionValue) to get coords from * @param ret * 2D vector / point with computed coords */ static public void multiplyMatrix(MyList list, VectorNDValue rt, GeoVec2D ret) { double a, b, c, d, e, f, xx, yy, zz; GeoVecInterface v = rt.getVector(); xx = v.getX(); yy = v.getY(); zz = v.getZ(); a = MyList.getCell(list, 0, 0).evaluateDouble(); b = MyList.getCell(list, 1, 0).evaluateDouble(); c = MyList.getCell(list, 2, 0).evaluateDouble(); d = MyList.getCell(list, 0, 1).evaluateDouble(); e = MyList.getCell(list, 1, 1).evaluateDouble(); f = MyList.getCell(list, 2, 1).evaluateDouble(); ret.setCoords(a * xx + b * yy + c * zz, d * xx + e * yy + f * zz); return; } @Override public int getMode() { return this.mode; } public Geo3DVec round() { return new Geo3DVec(kernel, Math.round(x), Math.round(y), Math.round(z)); } public Geo3DVec floor() { return new Geo3DVec(kernel, Math.floor(x), Math.floor(y), Math.floor(z)); } public Geo3DVec ceil() { return new Geo3DVec(kernel, Math.ceil(x), Math.ceil(y), Math.ceil(z)); } public ExpressionNode wrap() { return new ExpressionNode(kernel, this); } public double arg() { return Math.atan2(y, x); } }