我曾尝试实现第三人称摄影机倍增，但似乎无法正常工作。移动和缩放效果很好，但是旋转只会给我带来很多麻烦：
[更改摄影机的俯仰角（即，从观看播放器的高度看），摄影机始终围绕世界x轴在播放器的位置而不是摄影机x轴旋转
[改变播放器周围的角度时，相机始终绕着播放器的位置绕世界z轴旋转，而不是相机z轴旋转
当朝任何方向旋转相机时，它会沿所述方向缓慢移动，而不是与播放器位置保持固定的偏移量
我已经尝试过更改矩阵乘法的顺序，但这无济于事，我还尝试过查看矩阵，但这根本不起作用，会产生各种各样的其他问题。我知道，使用数学库会使这变得容易得多，但这不是我的目标。我至少想尝试理解其背后的数学原理并理解我的错误。
我的Matrix4f类：
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()));
}
}
和我的相机课：
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);
}
}
所以我设法解决了我的问题，作者
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);
改进的Camera类（我添加了浮点平滑以消除动作中的所有杂物）：
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);
}
}
改进的Matrix4f类：
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()));
}
}