I've tried implementing a 3rd person camera multiply times, but i just can't seem to get it to work. The movement and the zoom work fine, but the rotation just causes me a lot of troubles:
When changing the pitch of the camera (i.e. from how high you are looking at the player), the camera always rotates around the world x axis at the position of the player and not the camera x axis
When changing the angle around the player, the camera always rotates around the world z axis at the position of the player and not the camera z axis
When rotating the camera in any direction, it slowly moves in said direction, not staying at the fixed offset from the player position
I've already tried changing the matrix multiplication order, but that doesn't help and I've also tried using a look at matrix, but that wouldn't work at all, creating all sorts of other issues. I know, that using a math library would make this a lot easier, but that's not my goal. I want to at least try to understand the math behind this and understand my mistake.
My Matrix4f class:
import java.nio.FloatBuffer;
import java.util.Arrays;
import java.util.Iterator;
import com.engine.toolbox.ArrayUtils;
import com.engine.toolbox.BufferUtils;
import com.engine.toolbox.math.vectors.Vector3f;
import com.engine.toolbox.math.vectors.Vector4f;
public class Matrix4f extends Matrix{
public float m11, m12, m13, m14, m21, m22, m23, m24, m31, m32, m33, m34, m41, m42, m43, m44;
public Matrix4f(float m11, float m12, float m13, float m14,
float m21, float m22, float m23, float m24,
float m31, float m32, float m33, float m34,
float m41, float m42, float m43, float m44) {
super(new Float[] { m11, m12, m13, m14,
m21, m22, m23, m24,
m31, m32, m33, m34,
m41, m42, m43, m44});
this.m11 = m11;
this.m12 = m12;
this.m13 = m13;
this.m14 = m14;
this.m21 = m21;
this.m22 = m22;
this.m23 = m23;
this.m24 = m24;
this.m31 = m31;
this.m32 = m32;
this.m33 = m33;
this.m34 = m34;
this.m41 = m41;
this.m42 = m42;
this.m43 = m43;
this.m44 = m44;
}
@Override
public Iterator<Float> iterator() {
return Arrays.asList(this.toRawTypes()).iterator();
}
public Matrix4f invert() {
Matrix4f matrixOfMinors = new Matrix4f( new Matrix3f( m22, m23, m24,
m32, m33, m34,
m42, m43, m44).getDeterminant(), new Matrix3f( m21, m23, m24,
m31, m33, m34,
m41, m43, m44).getDeterminant(), new Matrix3f( m21, m22, m24,
m31, m32, m34,
m41, m42, m44).getDeterminant(), new Matrix3f( m21, m22, m23,
m31, m32, m33,
m41, m42, m43).getDeterminant(),
new Matrix3f( m12, m13, m14,
m32, m33, m34,
m42, m43, m44).getDeterminant(), new Matrix3f( m11, m13, m14,
m31, m33, m34,
m41, m43, m44).getDeterminant(), new Matrix3f( m11, m12, m14,
m31, m32, m34,
m41, m42, m44).getDeterminant(), new Matrix3f( m11, m12, m23,
m31, m32, m33,
m41, m42, m43).getDeterminant(),
new Matrix3f( m12, m13, m14,
m22, m23, m24,
m42, m43, m44).getDeterminant(), new Matrix3f( m11, m13, m14,
m21, m23, m24,
m41, m43, m44).getDeterminant(), new Matrix3f( m11, m12, m14,
m21, m22, m24,
m41, m42, m44).getDeterminant(), new Matrix3f( m11, m12, m23,
m21, m22, m23,
m41, m42, m43).getDeterminant(),
new Matrix3f( m12, m13, m14,
m22, m23, m24,
m32, m33, m34).getDeterminant(), new Matrix3f( m11, m13, m14,
m21, m23, m24,
m31, m33, m34).getDeterminant(), new Matrix3f( m11, m12, m14,
m21, m22, m24,
m31, m32, m34).getDeterminant(), new Matrix3f( m11, m12, m23,
m21, m22, m23,
m31, m32, m33).getDeterminant());
matrixOfMinors.m12 = -m12;
matrixOfMinors.m14 = -m14;
matrixOfMinors.m21 = -m21;
matrixOfMinors.m23 = -m23;
matrixOfMinors.m32 = -m32;
matrixOfMinors.m34 = -m34;
matrixOfMinors.m41 = -m41;
matrixOfMinors.m43 = -m43;
float temp = 0;
temp = matrixOfMinors.m12;
matrixOfMinors.m12 = matrixOfMinors.m21;
matrixOfMinors.m21 = temp;
temp = matrixOfMinors.m13;
matrixOfMinors.m13= matrixOfMinors.m31;
matrixOfMinors.m31 = temp;
temp = matrixOfMinors.m23;
matrixOfMinors.m23 = matrixOfMinors.m32;
matrixOfMinors.m32 = temp;
temp = matrixOfMinors.m14;
matrixOfMinors.m14 = matrixOfMinors.m41;
matrixOfMinors.m41 = temp;
temp = matrixOfMinors.m24;
matrixOfMinors.m24 = matrixOfMinors.m42;
matrixOfMinors.m42 = temp;
temp = matrixOfMinors.m34;
matrixOfMinors.m34 = matrixOfMinors.m43;
matrixOfMinors.m43 = temp;
float d = this.getDeterminant();
return new Matrix4f(matrixOfMinors.m11/d, matrixOfMinors.m12/d, matrixOfMinors.m13/d, matrixOfMinors.m14/d,
matrixOfMinors.m21/d, matrixOfMinors.m22/d, matrixOfMinors.m23/d, matrixOfMinors.m24/d,
matrixOfMinors.m31/d, matrixOfMinors.m32/d, matrixOfMinors.m33/d, matrixOfMinors.m34/d,
matrixOfMinors.m41/d, matrixOfMinors.m42/d, matrixOfMinors.m43/d, matrixOfMinors.m44/d);
}
public float getDeterminant() {
return m11*(new Matrix3f( m22, m23, m24,
m32, m33, m34,
m42, m43, m44).getDeterminant()) -
m12*(new Matrix3f( m21, m23, m24,
m31, m33, m34,
m41, m43, m44).getDeterminant()) +
m13*(new Matrix3f( m21, m22, m24,
m31, m32, m34,
m41, m42, m44).getDeterminant()) -
m14*(new Matrix3f( m21, m22, m23,
m31, m32, m33,
m41, m42, m43).getDeterminant());
}
public static Matrix4f identity() {
return new Matrix4f(1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1);
}
public static Matrix4f perspective(float aspectRatio, float viewAngle, float nearPlane, float farPlane) {
return new Matrix4f((float) (1/(aspectRatio*Math.tan((viewAngle/2)))), 0, 0, 0,
0, (float) (1/(Math.tan((viewAngle/2)))), 0, 0,
0, 0, -(farPlane+nearPlane)/(farPlane-nearPlane), (2*farPlane*nearPlane)/(farPlane-nearPlane),
0, 0, -1, 1);
}
public static Matrix4f translation(Vector3f translation) {
Matrix4f result = Matrix4f.identity();
result.m14 = translation.x;
result.m24 = translation.y;
result.m34 = translation.z;
return result;
}
public static Matrix4f scale(Vector3f scale) {
Matrix4f result = Matrix4f.identity();
result.m11 = scale.x;
result.m22 = scale.y;
result.m33 = scale.z;
return result;
}
public Matrix4f minus(Matrix4f m) {
return new Matrix4f(m11-m.m11, m12-m.m12, m13-m.m13, m14-m.m14,
m21-m.m21, m22-m.m22, m13-m.m23, m24-m.m24,
m31-m.m31, m32-m.m32, m13-m.m33, m34-m.m34,
m41-m.m41, m42-m.m42, m13-m.m43, m44-m.m44);
}
public Matrix4f plus(Matrix4f m) {
return new Matrix4f(m11+m.m11, m12+m.m12, m13+m.m13, m14+m.m14,
m21+m.m21, m22+m.m22, m13+m.m23, m24+m.m24,
m31+m.m31, m32+m.m32, m13+m.m33, m34+m.m34,
m41+m.m41, m42+m.m42, m13+m.m43, m44+m.m44);
}
public Matrix4f multiply(Matrix4f m) {
Vector4f r1 = new Vector4f(m11, m12, m13, m14);
Vector4f r2 = new Vector4f(m21, m22, m23, m24);
Vector4f r3 = new Vector4f(m31, m32, m33, m34);
Vector4f r4 = new Vector4f(m41, m42, m43, m44);
Vector4f c1 = new Vector4f(m.m11, m.m21, m.m31, m.m41);
Vector4f c2 = new Vector4f(m.m12, m.m22, m.m32, m.m42);
Vector4f c3 = new Vector4f(m.m13, m.m23, m.m33, m.m43);
Vector4f c4 = new Vector4f(m.m14, m.m24, m.m34, m.m44);
return new Matrix4f(r1.dot(c1), r1.dot(c2), r1.dot(c3), r1.dot(c4),
r2.dot(c1), r2.dot(c2), r2.dot(c3), r2.dot(c4),
r3.dot(c1), r3.dot(c2), r3.dot(c3), r3.dot(c4),
r4.dot(c1), r4.dot(c2), r4.dot(c3), r4.dot(c4));
}
public Vector4f multiply(Vector4f v) {
return new Vector4f(m11*v.x+m12*v.y+m13*v.z+m14*v.w,
m21*v.x+m22*v.y+m23*v.z+m24*v.w,
m31*v.x+m32*v.y+m33*v.z+m34*v.w,
m41*v.x+m42*v.y+m43*v.z+m44*v.w);
}
public static Matrix4f lookAt(Vector3f eye, Vector3f target, Vector3f up) {
Vector3f direction = eye.minus(target).normalize();
Vector3f right = direction.cross(up).normalize();
Vector3f camUp = right.cross(direction);
direction = direction.negate();
Matrix4f viewMatrix = new Matrix4f(
right.x, right.y, right.z, -right.dot(eye),
camUp.x, camUp.y, camUp.z, -camUp.dot(eye),
direction.x, direction.y, direction.z, -direction.dot(eye),
0, 0, 0, 1);
return viewMatrix;
}
public String toString() {
return "" + this.m11 + " " + this.m12 + " " + this.m13 + " " + this.m14 + "\n" +
this.m21 + " " + this.m22 + " " + this.m23 + " " + this.m24 + "\n" +
this.m31 + " " + this.m32 + " " + this.m33 + " " + this.m34 + "\n" +
this.m41 + " " + this.m42 + " " + this.m43 + " " + this.m44 + "\n";
}
public FloatBuffer toFloatBuffer() {
return BufferUtils.createFloatBuffer(ArrayUtils.toFloatArray(this.toRawTypes()));
}
}
And my camera class:
import com.engine.componentsystem.Component;
import com.engine.eventsystem.eventtypes.engineevents.UpdateEvent;
import com.engine.eventsystem.eventtypes.mouseevents.MouseMovedEvent;
import com.engine.eventsystem.eventtypes.mouseevents.MousePressedEvent;
import com.engine.eventsystem.eventtypes.mouseevents.MouseReleasedEvent;
import com.engine.eventsystem.eventtypes.mouseevents.MouseScrolledEvent;
import com.engine.toolbox.math.matrix.Matrix4f;
import com.engine.toolbox.math.quaternion.Quaternion;
import com.engine.toolbox.math.vectors.Vector3f;
public class CameraComponent extends Component{
private boolean right = false, left = false;
private float mouseX = 0, mouseY = 0, oldMouseX, oldMouseY;
private float distanceFromTarget = -5, angleAroundTarget;
private Vector3f position = new Vector3f(0.0f), rotation = new Vector3f(0.0f), target;
public CameraComponent() {}
public Vector3f getPosition() {
return position;
}
public Vector3f getRotation() {
return rotation;
}
public Vector3f getTarget() {
return target;
}
private float calculateHorizontalDistance() {
return (float) (this.distanceFromTarget*Math.cos(Math.toRadians(this.rotation.x)));
}
private float calculateVerticalDistance() {
return (float) (this.distanceFromTarget*Math.sin(Math.toRadians(this.rotation.x)));
}
public Matrix4f getViewMatrix() {
Matrix4f result = Matrix4f.identity();
Matrix4f rotationM = Quaternion.fromEuler(rotation).toMatrix();
Matrix4f translation = Matrix4f.translation(position.negate());
Matrix4f origin = Matrix4f.translation(target);
Matrix4f Iorigin = Matrix4f.translation(target.negate());
System.out.println("target: " + target);
System.out.println("position: " + position);
System.out.println("rotation: " + rotation);
result = result.multiply(translation);
result = result.multiply(origin);
result = result.multiply(rotationM);
result = result.multiply(Iorigin);
return result;
}
@Override
public void onAttach() {
this.target = ((PositionComponent) parent.getComponent(PositionComponent.class)).getPosition();
}
@Override
public boolean onMouseScrolled(MouseScrolledEvent event) {
this.distanceFromTarget += event.getyOffset()*0.7f;
return false;
}
@Override
public boolean onMousePressed(MousePressedEvent event) {
if(event.getButton() == 0 && event.getMods() == 1) {
left = true;
}
if(event.getButton() == 1 && event.getMods() == 1) {
right = true;
}
return false;
}
@Override
public boolean onMouseReleased(MouseReleasedEvent event) {
if(event.getButton() == 0) {
left = false;
}
if(event.getButton() == 1) {
right = false;
}
return false;
}
@Override
public boolean onMouseMoved(MouseMovedEvent event) {
oldMouseX = mouseX;
oldMouseY = mouseY;
mouseX = event.getX();
mouseY = event.getY();
if(left) {
this.angleAroundTarget -= (mouseX-oldMouseX)*0.01f;
}
if(right) {
this.rotation.x -= (mouseY-oldMouseY)*0.01f;
}
return false;
}
@Override
public void onUpdate(UpdateEvent event) {
this.target = ((PositionComponent) parent.getComponent(PositionComponent.class)).getPosition();
float horizantalDistance = calculateHorizontalDistance();
float verticalDistance = calculateVerticalDistance();
float theta = ((RotationComponent) parent.getComponent(RotationComponent.class)).getRotation().y + angleAroundTarget;
float xOffset = (float) (horizantalDistance*Math.sin(Math.toRadians(theta)));
float zOffset = (float) (horizantalDistance*Math.cos(Math.toRadians(theta)));
this.position.x = target.x - xOffset;
this.position.y = target.y + verticalDistance;
this.position.z = target.z - zOffset;
this.rotation.y = (float) (Math.toRadians(180.0f) - theta);
}
}
So I managed to fix my problem, by
result = result.rotate((float) -this.rotation.x, new Vector3f(1f, 0f, 0f));
result = result.rotate((float) this.rotation.y, new Vector3f(0f, 1f, 0f));
result = result.translate(position.negate());
roll = (float) Math.toRadians(roll);
pitch = (float) Math.toRadians(pitch);
yaw = (float) Math.toRadians(yaw);
The improved Camera class (I added float smoothing to remove all the jerkiness from the motions):
package com.assec.engine.componentsystem.components;
import com.assec.engine.componentsystem.Component;
import com.assec.engine.eventsystem.engineevents.UpdateEvent;
import com.assec.engine.eventsystem.mouseevents.MouseMovedEvent;
import com.assec.engine.eventsystem.mouseevents.MousePressedEvent;
import com.assec.engine.eventsystem.mouseevents.MouseReleasedEvent;
import com.assec.engine.eventsystem.mouseevents.MouseScrolledEvent;
import com.assec.engine.toolbox.math.SmoothFloat;
import com.assec.engine.toolbox.math.matrix.Matrix4f;
import com.assec.engine.toolbox.math.vectors.Vector3f;
public class CameraComponent extends Component{
private boolean right = false, left = false;
private float mouseX = 0.0f, mouseY = 0.0f, oldMouseX, oldMouseY;
private SmoothFloat distanceFromTarget = new SmoothFloat(-10.0f, 5.0f);
private SmoothFloat angleAroundTarget = new SmoothFloat(0.0f, 10.0f);
private SmoothFloat pitch = new SmoothFloat(0.0f, 10.0f);
private Vector3f position = new Vector3f(0.0f), rotation = new Vector3f(0.0f), target;
public CameraComponent() {}
public Vector3f getPosition() {
return position;
}
public Vector3f getRotation() {
return rotation;
}
public Vector3f getTarget() {
return target;
}
private float calculateHorizontalDistance() {
return (float) (this.distanceFromTarget.getActual()*Math.cos(Math.toRadians(this.rotation.x)));
}
private float calculateVerticalDistance() {
return (float) (this.distanceFromTarget.getActual()*Math.sin(Math.toRadians(this.rotation.x)));
}
public Matrix4f getViewMatrix() {
Matrix4f result = Matrix4f.identity();
this.target = new Vector3f(0.0f);
this.rotation.x = pitch.getActual();
this.rotation.x%= 360;
float horizontalDistance = calculateHorizontalDistance();
float verticalDistance = calculateVerticalDistance();
float theta = angleAroundTarget.getActual();
float xOffset = (float) (horizontalDistance*Math.sin(Math.toRadians(theta)));
float zOffset = (float) (horizontalDistance*Math.cos(Math.toRadians(theta)));
this.position.x = target.x - xOffset;
this.position.y = target.y + verticalDistance;
this.position.z = target.z - zOffset;
this.rotation.y = 360.0f - theta;
this.rotation.y%= 360;
result = result.rotate((float) -this.rotation.x, new Vector3f(1f, 0f, 0f));
result = result.rotate((float) this.rotation.y, new Vector3f(0f, 1f, 0f));
result = result.translate(position.negate());
return result;
}
@Override
public void onAttach() {
this.target = ((PositionComponent) parent.getComponent(PositionComponent.class)).getPosition();
this.target = new Vector3f(0.0f);
}
@Override
public boolean onMouseScrolled(MouseScrolledEvent event) {
this.distanceFromTarget.increaseTarget(-event.getyOffset()*0.7f);
return false;
}
@Override
public boolean onMousePressed(MousePressedEvent event) {
if(event.getButton() == 0 && event.getMods() == 1) {
left = true;
}
if(event.getButton() == 1 && event.getMods() == 1) {
right = true;
}
return false;
}
@Override
public boolean onMouseReleased(MouseReleasedEvent event) {
if(event.getButton() == 0) {
left = false;
}
if(event.getButton() == 1) {
right = false;
}
return false;
}
@Override
public boolean onMouseMoved(MouseMovedEvent event) {
oldMouseX = mouseX;
oldMouseY = mouseY;
mouseX = (float) event.getX();
mouseY = (float) event.getY();
if(left) {
this.angleAroundTarget.increaseTarget(-(mouseX-oldMouseX)*0.1f);
}
if(right) {
this.pitch.increaseTarget(-(mouseY-oldMouseY)*0.1f);
}
return false;
}
@Override
public void onUpdate(UpdateEvent event) {
this.angleAroundTarget.update(0.01f);
this.distanceFromTarget.update(0.01f);
this.pitch.update(0.01f);
}
}
The improved Matrix4f class:
package com.assec.engine.toolbox.math.matrix;
import java.nio.FloatBuffer;
import java.util.Arrays;
import java.util.Iterator;
import com.assec.engine.toolbox.ArrayUtils;
import com.assec.engine.toolbox.BufferUtils;
import com.assec.engine.toolbox.math.quaternion.Quaternion;
import com.assec.engine.toolbox.math.vectors.Vector3f;
import com.assec.engine.toolbox.math.vectors.Vector4f;
public class Matrix4f extends Matrix{
public float m11, m12, m13, m14, m21, m22, m23, m24, m31, m32, m33, m34, m41, m42, m43, m44;
public Matrix4f(float m11, float m12, float m13, float m14,
float m21, float m22, float m23, float m24,
float m31, float m32, float m33, float m34,
float m41, float m42, float m43, float m44) {
super(new Float[] { m11, m12, m13, m14,
m21, m22, m23, m24,
m31, m32, m33, m34,
m41, m42, m43, m44});
this.m11 = m11;
this.m12 = m12;
this.m13 = m13;
this.m14 = m14;
this.m21 = m21;
this.m22 = m22;
this.m23 = m23;
this.m24 = m24;
this.m31 = m31;
this.m32 = m32;
this.m33 = m33;
this.m34 = m34;
this.m41 = m41;
this.m42 = m42;
this.m43 = m43;
this.m44 = m44;
}
@Override
public Iterator<Float> iterator() {
return Arrays.asList(this.toRawTypes()).iterator();
}
public Matrix4f invert() {
Matrix4f matrixOfMinors = new Matrix4f( new Matrix3f( m22, m23, m24,
m32, m33, m34,
m42, m43, m44).getDeterminant(), new Matrix3f( m21, m23, m24,
m31, m33, m34,
m41, m43, m44).getDeterminant(), new Matrix3f( m21, m22, m24,
m31, m32, m34,
m41, m42, m44).getDeterminant(), new Matrix3f( m21, m22, m23,
m31, m32, m33,
m41, m42, m43).getDeterminant(),
new Matrix3f( m12, m13, m14,
m32, m33, m34,
m42, m43, m44).getDeterminant(), new Matrix3f( m11, m13, m14,
m31, m33, m34,
m41, m43, m44).getDeterminant(), new Matrix3f( m11, m12, m14,
m31, m32, m34,
m41, m42, m44).getDeterminant(), new Matrix3f( m11, m12, m23,
m31, m32, m33,
m41, m42, m43).getDeterminant(),
new Matrix3f( m12, m13, m14,
m22, m23, m24,
m42, m43, m44).getDeterminant(), new Matrix3f( m11, m13, m14,
m21, m23, m24,
m41, m43, m44).getDeterminant(), new Matrix3f( m11, m12, m14,
m21, m22, m24,
m41, m42, m44).getDeterminant(), new Matrix3f( m11, m12, m23,
m21, m22, m23,
m41, m42, m43).getDeterminant(),
new Matrix3f( m12, m13, m14,
m22, m23, m24,
m32, m33, m34).getDeterminant(), new Matrix3f( m11, m13, m14,
m21, m23, m24,
m31, m33, m34).getDeterminant(), new Matrix3f( m11, m12, m14,
m21, m22, m24,
m31, m32, m34).getDeterminant(), new Matrix3f( m11, m12, m23,
m21, m22, m23,
m31, m32, m33).getDeterminant());
matrixOfMinors.m12 = -m12;
matrixOfMinors.m14 = -m14;
matrixOfMinors.m21 = -m21;
matrixOfMinors.m23 = -m23;
matrixOfMinors.m32 = -m32;
matrixOfMinors.m34 = -m34;
matrixOfMinors.m41 = -m41;
matrixOfMinors.m43 = -m43;
float temp = 0;
temp = matrixOfMinors.m12;
matrixOfMinors.m12 = matrixOfMinors.m21;
matrixOfMinors.m21 = temp;
temp = matrixOfMinors.m13;
matrixOfMinors.m13= matrixOfMinors.m31;
matrixOfMinors.m31 = temp;
temp = matrixOfMinors.m23;
matrixOfMinors.m23 = matrixOfMinors.m32;
matrixOfMinors.m32 = temp;
temp = matrixOfMinors.m14;
matrixOfMinors.m14 = matrixOfMinors.m41;
matrixOfMinors.m41 = temp;
temp = matrixOfMinors.m24;
matrixOfMinors.m24 = matrixOfMinors.m42;
matrixOfMinors.m42 = temp;
temp = matrixOfMinors.m34;
matrixOfMinors.m34 = matrixOfMinors.m43;
matrixOfMinors.m43 = temp;
float d = this.getDeterminant();
return new Matrix4f(matrixOfMinors.m11/d, matrixOfMinors.m12/d, matrixOfMinors.m13/d, matrixOfMinors.m14/d,
matrixOfMinors.m21/d, matrixOfMinors.m22/d, matrixOfMinors.m23/d, matrixOfMinors.m24/d,
matrixOfMinors.m31/d, matrixOfMinors.m32/d, matrixOfMinors.m33/d, matrixOfMinors.m34/d,
matrixOfMinors.m41/d, matrixOfMinors.m42/d, matrixOfMinors.m43/d, matrixOfMinors.m44/d);
}
public float getDeterminant() {
return m11*(new Matrix3f( m22, m23, m24,
m32, m33, m34,
m42, m43, m44).getDeterminant()) -
m12*(new Matrix3f( m21, m23, m24,
m31, m33, m34,
m41, m43, m44).getDeterminant()) +
m13*(new Matrix3f( m21, m22, m24,
m31, m32, m34,
m41, m42, m44).getDeterminant()) -
m14*(new Matrix3f( m21, m22, m23,
m31, m32, m33,
m41, m42, m43).getDeterminant());
}
public static Matrix4f identity() {
return new Matrix4f(1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1);
}
public static Matrix4f perspective(float aspectRatio, float viewAngle, float nearPlane, float farPlane) {
return new Matrix4f((float) (1/(aspectRatio*Math.tan((viewAngle/2)))), 0, 0, 0,
0, (float) (1/(Math.tan((viewAngle/2)))), 0, 0,
0, 0, -((farPlane+nearPlane)/(farPlane-nearPlane)), -(2*farPlane*nearPlane)/(farPlane-nearPlane),
0, 0, -1, 1);
}
public static Matrix4f translation(Vector3f translation) {
Matrix4f result = Matrix4f.identity();
result.m14 = translation.x;
result.m24 = translation.y;
result.m34 = translation.z;
return result;
}
public static Matrix4f scale(Vector3f scale) {
Matrix4f result = Matrix4f.identity();
result.m11 = scale.x;
result.m22 = scale.y;
result.m33 = scale.z;
return result;
}
public Matrix4f minus(Matrix4f m) {
return new Matrix4f(m11-m.m11, m12-m.m12, m13-m.m13, m14-m.m14,
m21-m.m21, m22-m.m22, m13-m.m23, m24-m.m24,
m31-m.m31, m32-m.m32, m13-m.m33, m34-m.m34,
m41-m.m41, m42-m.m42, m13-m.m43, m44-m.m44);
}
public Matrix4f plus(Matrix4f m) {
return new Matrix4f(m11+m.m11, m12+m.m12, m13+m.m13, m14+m.m14,
m21+m.m21, m22+m.m22, m13+m.m23, m24+m.m24,
m31+m.m31, m32+m.m32, m13+m.m33, m34+m.m34,
m41+m.m41, m42+m.m42, m13+m.m43, m44+m.m44);
}
public Matrix4f multiply(Matrix4f m) {
Vector4f r1 = new Vector4f(m11, m12, m13, m14);
Vector4f r2 = new Vector4f(m21, m22, m23, m24);
Vector4f r3 = new Vector4f(m31, m32, m33, m34);
Vector4f r4 = new Vector4f(m41, m42, m43, m44);
Vector4f c1 = new Vector4f(m.m11, m.m21, m.m31, m.m41);
Vector4f c2 = new Vector4f(m.m12, m.m22, m.m32, m.m42);
Vector4f c3 = new Vector4f(m.m13, m.m23, m.m33, m.m43);
Vector4f c4 = new Vector4f(m.m14, m.m24, m.m34, m.m44);
return new Matrix4f(r1.dot(c1), r1.dot(c2), r1.dot(c3), r1.dot(c4),
r2.dot(c1), r2.dot(c2), r2.dot(c3), r2.dot(c4),
r3.dot(c1), r3.dot(c2), r3.dot(c3), r3.dot(c4),
r4.dot(c1), r4.dot(c2), r4.dot(c3), r4.dot(c4));
}
public Vector4f multiply(Vector4f v) {
return new Vector4f(m11*v.x+m12*v.y+m13*v.z+m14*v.w,
m21*v.x+m22*v.y+m23*v.z+m24*v.w,
m31*v.x+m32*v.y+m33*v.z+m34*v.w,
m41*v.x+m42*v.y+m43*v.z+m44*v.w);
}
public Matrix4f rotate(float angle, Vector3f axis) {
Matrix4f rotation = Quaternion.fromEuler(axis.normalized().scaled(angle)).toMatrix();
return this.multiply(rotation);
}
public Matrix4f translate(Vector3f translation) {
Matrix4f translate = Matrix4f.translation(translation);
return this.multiply(translate);
}
public static Matrix4f lookAt(Vector3f eye, Vector3f target, Vector3f up) {
Vector3f direction = eye.minus(target).normalized();
Vector3f right = direction.cross(up).normalized();
Vector3f camUp = right.cross(direction);
direction = direction.negate();
Matrix4f viewMatrix = new Matrix4f(
right.x, right.y, right.z, -right.dot(eye),
camUp.x, camUp.y, camUp.z, -camUp.dot(eye),
direction.x, direction.y, direction.z, -direction.dot(eye),
0.0f, 0.0f, 0.0f, 1.0f);
return viewMatrix;
}
public String toString() {
return "" + this.m11 + " " + this.m12 + " " + this.m13 + " " + this.m14 + "\n" +
this.m21 + " " + this.m22 + " " + this.m23 + " " + this.m24 + "\n" +
this.m31 + " " + this.m32 + " " + this.m33 + " " + this.m34 + "\n" +
this.m41 + " " + this.m42 + " " + this.m43 + " " + this.m44 + "\n";
}
public FloatBuffer toFloatBuffer() {
return BufferUtils.createFloatBuffer(ArrayUtils.toFloatArray(this.toRawTypes()));
}
}