I’m not very experienced with Java or computer graphics, but I thought I’d try and program a rough 3D engine in Java as I’ve been finding APCS pretty fun. I’ve gotten as far as implementing vertices, triangles, face culling, and rotation/translation matrices, but I can’t for the life of me figure out how to do a projection matrix.
I have a 4×4 matrix class:
public class Matrix4 {
double[][] m = new double[4][4];
public Matrix4 (double[][] nm) {
for (int r = 0; r < nm.length; r++) {
for (int c = 0; c < nm[r].length; c++) {
m[r][c] = nm[r][c];
}
}
}
public Vertex multiplyMatrix(Vertex v) {
Vertex o = new Vertex(0, 0, 0);
o.x = v.x * m[0][0] + v.y * m[1][0] + v.z * m[2][0] + m[3][0];
o.y = v.x * m[0][1] + v.y * m[1][1] + v.z * m[2][1] + m[3][1];
o.z = v.x * m[0][2] + v.y * m[1][2] + v.z * m[2][2] + m[3][2];
double w = v.x * m[0][3] + v.y * m[1][3] + v.z * m[2][3] + m[3][3];
if (w != 0) {
o.x /= w;
o.y /= w;
o.z /= w;
}
System.out.println(o);
return o;
}
}
and using this I have created a projection matrix copied from videos/images I’ve seen online:
private double fNear = 0.1;
private double fFar = 1000;
private double fFOV = 50;
private double fAspectRatio = (double)width/height;
private double fFOVRad = 1 / Math.tan(Math.toRadians(fFOV / 2));
matProj = new Matrix4(new double[][]{
{fAspectRatio * fFOVRad,0, 0, 0},
{0, fFOVRad, 0, 0},
{0, 0, (fFar + fNear) / (fFar - fNear), 1},
{0, 0, (-2 * fFar * fNear) / (fFar - fNear),0}});
To render the triangles, I’m going through the list of triangles and one-by-one multiplying their vertices by this projection matrix, and then printing them to the screen:
public void paintComponent(Graphics g) {
super.paintComponent(g);
for (int i = 0; i < triangleList.size(); i++) {
Triangle triangle = new Triangle(triangleList.get(i).v1, triangleList.get(i).v2, triangleList.get(i).v3);
if (!triangle.cullTriangle(cameraVector)) {
g.setColor(colorList.get(i));
triangle.v1 = matProj.multiplyMatrix(triangle.v1);
triangle.v2 = matProj.multiplyMatrix(triangle.v2);
triangle.v3 = matProj.multiplyMatrix(triangle.v3);
int[] vX = {width / 2 + (int)(triangle.v1.x),
width / 2 + (int)(triangle.v2.x),
width / 2 + (int)(triangle.v3.x)};
int[] vY = {height / 2 - (int)(triangle.v1.z),
height / 2 - (int)(triangle.v2.z),
height / 2 - (int)(triangle.v3.z)};
g.fillPolygon(vX, vY, 3);
}
}
}
However, this isn’t working at all, and it’s just fragmenting the shape into thin strips and glitches. If I just comment out the three matProj.multiplyMatrix lines, everything works as it should but without perspective. I’m sure this is a really stupid issue, but I’m new to this type of stuff and I’m really stumped right now, so any help would be great!
Here is my full main class if needed:
import java.io.*;
import java.lang.Math;
import java.awt.*;
import java.awt.event.*;
import javax.swing.*;
import java.util.ArrayList;
import java.awt.PointerInfo;
public class main extends JPanel implements ActionListener, MouseListener {
private Timer timer;
public int time;
public JFrame frame;
public int width = 500, height = 500;
private double[] mouseDown;
private double[] mouseMoved;
private boolean isRotating = false;
private double[] viewVertex = {0, 0, 0};
private double[] worldPos = {0, 0, 0};
private Point pointer;
private boolean inTranslateMode = false; //movement modes
private double fNear = 0.1;
private double fFar = 1000;
private double fFOV = 50;
private double fAspectRatio = (double)width/height;
private double fFOVRad = 1 / Math.tan(Math.toRadians(fFOV / 2));
ArrayList<Triangle> triangleList; //List of triangles
ArrayList<Color> colorList; //List of polygon colors
private Vertex cameraVector; //Vector of the player/camera
private double fov = Math.toRadians(60); // Field of view in radians
private double near = 1; // Near clipping plane distance
private double far = 1000;
private Matrix4 matProj;
public main () {
mouseDown = new double[2];
mouseMoved = new double[2];
triangleList = new ArrayList<>();
colorList = new ArrayList<>();
//Player vector
cameraVector = new Vertex(0, 1, 0);
Cube cube1 = new Cube(50, 1, 1, 1);
cube1.add(triangleList, colorList);
for (Triangle t : triangleList) {
t.translate(worldPos[0], worldPos[1], worldPos[2]);
}
//set up JFrame
frame = new JFrame("3D Engine");
frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
setLayout(new FlowLayout());
setPreferredSize(new Dimension(width, height));
setBackground(Color.WHITE);
frame.add(this);
addMouseListener(this);
frame.pack();
frame.setVisible(true);
setFocusable(true);
timer = new Timer(10, this);
timer.start();
time = 0;
matProj = new Matrix4(new double[][]{
{fAspectRatio * fFOVRad,0, 0, 0},
{0, fFOVRad, 0, 0},
{0, 0, (fFar + fNear) / (fFar - fNear), 1},
{0, 0, (-2 * fFar * fNear) / (fFar - fNear),0}});
addKeyListener(new KeyAdapter() {
public void keyPressed(KeyEvent e) {
if (e.getKeyCode() == KeyEvent.VK_RIGHT) {
if (inTranslateMode) {
for (Triangle t : triangleList) {
t.translate(5, 0, 0);
}
} else {
for (Triangle t : triangleList) {
t.rotateZ(10);
}
}
} else if (e.getKeyCode() == KeyEvent.VK_LEFT) {
if (inTranslateMode) {
for (Triangle t : triangleList) {
t.translate(-5, 0, 0);
}
} else {
for (Triangle t : triangleList) {
t.rotateZ(-10);
}
}
} else if (e.getKeyCode() == KeyEvent.VK_UP) {
if (inTranslateMode) {
for (Triangle t : triangleList) {
t.translate(0, 5, 0);
}
} else {
for (Triangle t : triangleList) {
t.rotateX(10);
}
}
} else if (e.getKeyCode() == KeyEvent.VK_DOWN) {
if (inTranslateMode) {
for (Triangle t : triangleList) {
t.translate(0, -5, 0);
}
} else {
for (Triangle t : triangleList) {
t.rotateX(-10);
}
}
} else if (e.getKeyCode() == KeyEvent.VK_SPACE) {
inTranslateMode = !inTranslateMode;
}
}
});
}
public void actionPerformed(ActionEvent e) {
repaint();
time++;
pointer = MouseInfo.getPointerInfo().getLocation();
if (isRotating) {
mouseMoved[0] = pointer.x - mouseDown[0];
mouseMoved[1] = pointer.y - mouseDown[1];
for (Triangle t : triangleList) {
t.rotateX(mouseMoved[0] / 5);
}
mouseDown[0] = pointer.x;
mouseDown[1] = pointer.y;
}
}
public void paintComponent(Graphics g) {
super.paintComponent(g);
for (int i = 0; i < triangleList.size(); i++) {
Triangle triangle = new Triangle(triangleList.get(i).v1, triangleList.get(i).v2, triangleList.get(i).v3);
if (!triangle.cullTriangle(cameraVector)) {
g.setColor(colorList.get(i));
triangle.v1 = matProj.multiplyMatrix(triangle.v1);
triangle.v2 = matProj.multiplyMatrix(triangle.v2);
triangle.v3 = matProj.multiplyMatrix(triangle.v3);
int[] vX = {width / 2 + (int)(triangle.v1.x),
width / 2 + (int)(triangle.v2.x),
width / 2 + (int)(triangle.v3.x)};
int[] vY = {height / 2 - (int)(triangle.v1.z),
height / 2 - (int)(triangle.v2.z),
height / 2 - (int)(triangle.v3.z)};
g.fillPolygon(vX, vY, 3);
}
}
}
public void mouseClicked(MouseEvent e) {}
public void mousePressed(MouseEvent e) {
isRotating = true;
mouseDown[0] = pointer.x;
mouseDown[1] = pointer.y;
}
public void mouseReleased(MouseEvent e) {
isRotating = false;
}
public void mouseEntered(MouseEvent e) {}
public void mouseExited(MouseEvent e) {}
public static void main (String[] args) {
new main();
}
}
I logged the vertex values within the matrix multiply method, and they are incorrect, so I assume it’s an issue with the multiplication if that helps. I also don’t know if I’m drawing them onto the screen correctly since Java uses a weird coordinate system (at least to me).
What I’m expecting is for shapes to be smaller when further away, and to be warped correctly into the screen to show depth. What happened instead is a bunch of this:
3d rendered cube fragments
and without the projection matrix multiplication, it looks like this:
Very minimal but cube-like cube
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