How to rotate one point ? - Page 1

       | _
    .M |   \-50° par exemple
       |   V
-------+-------
       |
       |
       |

x'=x
y'=cos(angle_x)*y-sin(angle_x)*z
z'=sin(angle_x)*y+cos(angle_x)*z

x'=cos(angle_y)*x+sin(angle_y)*z
y'=y
z'=-sin(angle_y)*x+cos(angle_y)*z

x'=cos(angle_z)*x-sin(angle_z)*y
y'=sin(angle_z)*x+cos(angle_z)*y
z'=z

yf=cos(angle_x)*y-sin(angle_x)*z
zf=sin(angle_x)*y+cos(angle_x)*z
xf=cos(angle_y)*x+sin(angle_y)*z
zf=-sin(angle_y)*x+cos(angle_y)*z
xf=cos(angle_z)*x-sin(angle_z)*y
yf=sin(angle_z)*x+cos(angle_z)*y

yf=cos(angle_x)*y-sin(angle_x)*z
zf=sin(angle_x)*y+cos(angle_x)*z
xf=cos(angle_y)*x+sin(angle_y)*zf
zff=-sin(angle_y)*x+cos(angle_y)*zf
xff=cos(angle_z)*xf-sin(angle_z)*yf
yff=sin(angle_z)*xf+cos(angle_z)*yf

[4][b][u]ROTATION D'AXE X:[/u][/b][/4]

x'=x
y'=cos(ax)*y-sin(ax)*z
z'=sin(ax)*y+cos(ax)*z

|1     0        0   |
|0  cos(ax) -sin(ax)|
|0  sin(ax)  cos(ax)|

[4][b][u]ROTATION D'AXE Y:[/u][/b][/4]

x'=cos(angle_y)*x+sin(angle_y)*z
y'=y
z'=-sin(angle_y)*x+cos(angle_y)*z

|cos(ay)   0   sin(ay)|
|   0      1      0   |
|-sin(ay)  0   cos(ay)|

[4][b][u]ROTATION D'AXE Z:[/u][/b][/4]

x'=cos(angle_z)*x-sin(angle_z)*y
y'=sin(angle_z)*x+cos(angle_z)*y
z'=z

|cos(az) -sin(az)  0|
|sin(az)  cos(az)  0|
|   0        0     1|

|a , b , c|   |1 , 2 , 3|   |1*a+4*b+7*c , 2*a+5*b+8*c , 3*a+6*b+9*c|
|d , e , f| . |4 , 5 , 6| = |1*d+4*e+7*f , 2*d+5*e+8*f , 3*d+6*e+9*f|
|g , h , i|   |7 , 8 , 9|   |1*g+4*h+7*i , 2*g+5*h+8*i , 3*g+6*h+9*i|

|Cos[Za]*Cos[Ya]  Cos[Za]*Sin[Ya]*Sin[Xa] - Sin[Za]*Cos[Xa]  Cos[Za]*Sin[Ya]*Cos[Xa] + Sin[Za]*Sin[Xa]|
|Sin[Za]*Cos[Ya]  Sin[Za]*Sin[Ya]*Sin[Xa] + Cos[Xa]*Cos[Za]  Sin[Za]*Sin[Ya]*Cos[Xa] - Cos[Za]*Sin[Xa]|
|   -Sin[Ya]                   Sin[Xa]*Cos[Ya]                          Cos[Xa]*Cos[Ya]               |

import javax.swing.*;
import java.awt.*;
import java.awt.event.*;
import java.awt.geom.*;

public class JCube extends JApplet {

	private Graphics2D g2D;
	private double xcenter;
	private double ycenter;
	private double povx;
	private double povy;
	private double povz;
	private Point3D[] pointarray = {
		new Point3D(-100.0, 100.0, 100.0),
		new Point3D(100.0, 100.0, 100.0),
		new Point3D(100.0, 100.0, -100.0),
		new Point3D(-100.0, 100.0, -100.0),
		new Point3D(-100.0, -100.0, 100.0),
		new Point3D(100.0, -100.0, 100.0),
		new Point3D(100.0, -100.0, -100.0),
		new Point3D(-100.0, -100.0, -100.0),
		new Point3D(-450.0, 0.0, 0.0),
		new Point3D(450.0, 0.0, 0.0),
		new Point3D(0.0, -450.0, 0.0),
		new Point3D(0.0, 450.0, 0.0),
		new Point3D(0.0, 0.0, -450.0),
		new Point3D(0.0, 0.0, 450.0)
	};

	private int[][] trianglearray = {
/*		{0, 1, 2},
		{2, 3, 0},
		{4, 5, 6},
		{6, 7, 4},
		{0, 1, 5},
		{0, 4, 5},
		{1, 2, 6},
		{1, 5, 6},
		{2, 3, 6},
		{3, 6, 7},
		{0, 4, 7},
		{0, 3, 7},
*/		{0, 3, 8},
		{0, 4, 8},
		{4, 7, 8},
		{3, 7, 8},
		{1, 2, 9},
		{1, 5, 9},
		{2, 6, 9},
		{5, 6, 9},
		{4, 5, 10},
		{4, 7, 10},
		{5, 6, 10},
		{6, 7, 10},
		{0, 1, 11},
		{1, 2, 11},
		{2, 3, 11},
		{3, 4, 11},
		{2, 3, 12},
		{2, 6, 12},
		{3, 7, 12},
		{6, 7, 12},
		{0, 1, 13},
		{1, 5, 13},
		{4, 5, 13},
		{0, 4, 13}
	};

	public void init() {
		povx = 0;
		povy = 0;
		povz = -500;
		xcenter = 500 / 2;
		ycenter = 500 / 2;
		this.setBounds(0, 0, 500, 500);
	}

	public void paint(Graphics g) {
		g2D = (Graphics2D)g;
		g2D.setPaint(Color.red);
		move();
	}

	public void renderPoint(Point3D p3d) {
		double x1 = (double)p3d.getX();
		double y1 = (double)p3d.getY();
		double z1 = -500.0 / (-1000.0 - (double)p3d.getZ());
		Rectangle2D.Double l1 = new Rectangle2D.Double(x1 * z1  + xcenter, y1 * z1  + ycenter, 1.0, 1.0);
		g2D.draw(l1);
	}

	public void renderLine(Point3D p3d1, Point3D p3d2) {
		double x1 = (double)p3d1.getX();
		double y1 = (double)p3d1.getY();
		double z1 = -500.0 / (-1000.0 - (double)p3d1.getZ());
		double x2 = (double)p3d2.getX();
		double y2 = (double)p3d2.getY();
		double z2 = -500.0 / (-1000.0 - (double)p3d2.getZ());
		Line2D.Double l1 = new Line2D.Double(x1 * z1  + xcenter, y1 * z1  + ycenter, x2 * z2  + xcenter, y2 * z2  + ycenter);
		g2D.draw(l1);
	}

	public void renderTriangle(Point3D p3d1, Point3D p3d2, Point3D p3d3) {
		double x1 = (double)p3d1.getX();
		double y1 = (double)p3d1.getY();
		double z1 = -500.0 / (-1000.0 - (double)p3d1.getZ());
		double x2 = (double)p3d2.getX();
		double y2 = (double)p3d2.getY();
		double z2 = -500.0 / (-1000.0 - (double)p3d2.getZ());
		double x3 = (double)p3d3.getX();
		double y3 = (double)p3d3.getY();
		double z3 = -500.0 / (-1000.0 - (double)p3d3.getZ());
		int[] tabx = {(int)(x1 * z1  + xcenter), (int)(x2 * z2  + xcenter), (int)(x3 * z3  + xcenter)};
		int[] taby = {(int)(y1 * z1  + ycenter), (int)(y2 * z2  + ycenter), (int)(y3 * z3  + ycenter)};
		g2D.fillPolygon(new Polygon(tabx, taby, 3));
	}

	public void renderObject() {
		for (int i = 0 ; i < trianglearray.length ; i++) {
			renderTriangle(pointarray[trianglearray[i][0]], pointarray[trianglearray[i][1]], pointarray[trianglearray[i][2]]);
		}
	}

	public void move() {
		while (true) {
			for (int j = 0 ; j < 360 ; j++) {
				for (int i = 0 ; i < pointarray.length ; i++) {
					pointarray[i] = RotatePointAroundAxes(pointarray[i], Math.PI / 101, Math.PI / 171, Math.PI / 343);
				}
				g2D.clearRect(0, 0, 500, 500);
// je repete 20 fois pour ralentir , j'ai pas encore trouvé comment faire un wait en java
				renderObject();
				renderObject();
				renderObject();
				renderObject();
				renderObject();
				renderObject();
				renderObject();
				renderObject();
				renderObject();
				renderObject();
				renderObject();
				renderObject();
				renderObject();
				renderObject();
				renderObject();
			}
		}
	}

	public Point3D RotatePointAroundAxes(Point3D p3d, double alphax, double alphay, double alphaz) {
		double x = p3d.getX();
		double y = p3d.getY();
		double z = p3d.getZ();
		p3d.setY(y * Math.cos(alphax) + z * Math.sin(alphax));
		p3d.setZ(-y * Math.sin(alphax) + z * Math.cos(alphax));
		x = p3d.getX();
		y = p3d.getY();
		z = p3d.getZ();
		p3d.setX(x * Math.cos(alphay) + z * Math.sin(alphay));
		p3d.setZ(-x * Math.sin(alphay) + z * Math.cos(alphay));
		x = p3d.getX();
		y = p3d.getY();
		z = p3d.getZ();
		p3d.setX(x * Math.cos(alphaz) + y * Math.sin(alphaz));
		p3d.setY(-x * Math.sin(alphaz) + y * Math.cos(alphaz));
		return p3d;
	}


	public class Point3D {

		private double x;
		private double y;
		private double z;

		public Point3D(double x, double y, double z) {
			this.setX(x);
			this.setY(y);
			this.setZ(z);
		}

		public double getX() {
			return this.x;
		}

		public double getY() {
			return this.y;
		}

		public double getZ() {
			return this.z;
		}

		public void setX(double value) {
			 this.x = value;
		}

		public void setY(double value) {
			 this.y = value;
		}

		public void setZ(double value) {
			 this.z = value;
		}
	}
}