java - 为什么我的旋转矩阵会产生额外的平移？

Question

几周前，我决定制作自己的简单 3D 游戏引擎。我在网上学习了一些教程，也看了很多视频，到目前为止，我已经得到了相当不错的引擎。但我有一个问题。当我旋转或缩放对象时，它的中心似乎是屏幕的左上角而不是其真正的中心。例如，当我旋转一个对象时，它会围绕屏幕的左边缘旋转，而当我缩放它时，它会向屏幕的一角或远离屏幕的一角缩放。这是我的代码:

网格类

package com.cub.cubefront.mesh;

import com.cub.cubefront.math.Matrix4f;
import com.cub.cubefront.math.Vector3f;

public class Mesh {

    private Vector3f[] verts;
    private Vector3f center;

    private double rotX = 0;
    private double rotY = 0;
    private double rotZ = 0;

    private double scaleX = 1;
    private double scaleY = 1;
    private double scaleZ = 1;

    private double translateX = 0;
    private double translateY = 0;
    private double translateZ = 0;

public Mesh(int arg0) {
    verts = new Vector3f[arg0];
}

public Vector3f getVertexAt(int arg0) {
    return verts[arg0 - 1];
}

public Vector3f[] getVerticies() {
    return verts;
}

public int getVerticiesCount() {
    return verts.length;
}

public void setVertexAt(int arg0, Vector3f arg1) {
    verts[arg0 - 1] = arg1;
}

public void setRotationPoint(Vector3f arg0) {
    this.center = arg0;
}

public Vector3f getRotationPoint() {
    return center;
}

public Vector3f getCenter() {
    int arg0 = verts.length;
    double centerX = 0;
    double centerY = 0;
    double centerZ = 0;
    for (int i = 0; i < arg0; i++) {
        centerX += verts[i].getX();
        centerY += verts[i].getY();
        centerZ += verts[i].getZ();
    }
    return new Vector3f((float)(centerX / arg0), (float)(centerY / arg0), (float)(centerZ / arg0));
}

public void rotateX(double arg0) {
    this.rotX += Math.toRadians(arg0);
}

public void setRotationX(double arg0) {
    this.rotX = Math.toRadians(arg0);
}

public Matrix4f getXRotationAsMatrix() {
    return new Matrix4f(new double[][] { // YZ rotation matrix (X)
        { 1, 0, 0, 0 },
        { 0, Math.cos(rotX), Math.sin(rotX), 0 },
        { 0, -Math.sin(rotX), Math.cos(rotX), 0 },
        { 0, 0, 0, 1 }
    });
}

public Matrix4f getZRotationAsMatrix() {
    return new Matrix4f(new double[][] { // XY rotation matrix (Z)
        { Math.cos(rotZ), -Math.sin(rotZ), 0, 0 },
        { Math.sin(rotZ), Math.cos(rotZ), 0, 0 },
        { 0, 0, 1, 0 },
        { 0, 0, 0, 1 }
    });
}

public void rotateY(double arg0) {
    this.rotY += Math.toRadians(arg0);
}

public void setRotationY(double arg0) {
    this.rotY = Math.toRadians(arg0);
}

public Matrix4f getYRotationAsMatrix() {
    return new Matrix4f(new double[][] { // XZ rotation matrix (Y)
        { Math.cos(rotY), 0, Math.sin(rotY), 0 },
        { 0, 1, 0, 0 },
        { -Math.sin(rotY), 0, Math.cos(rotY), 0},
        { 0, 0, 0, 1 }
    });
}

public void setRotationZ(double arg0) {
    this.rotZ = Math.toRadians(arg0);
}

public void rotateZ(double arg0) {
    this.rotZ += Math.toRadians(arg0);
}

public Matrix4f getRotation() {
    return getZRotationAsMatrix().multiply(getXRotationAsMatrix()).multiply(getYRotationAsMatrix());
}

public void setScaleX(double arg0) {
    this.scaleX = arg0;
}

public void scaleX(double arg0) {
    this.scaleX += arg0;
}

public double getScaleX() {
    return scaleX;
}

public void setScaleY(double arg0) {
    this.scaleY = arg0;
}

public void scaleY(double arg0) {
    this.scaleY += arg0;
}

public double getScaleY() {
    return scaleY;
}

public void setScaleZ(double arg0) {
    this.scaleZ = arg0;
}

public void scaleZ(double arg0) {
    this.scaleZ += arg0;
}

public double getScaleZ() {
    return scaleZ;
}

public void setScale(double arg0) {
    setScaleX(arg0);
    setScaleY(arg0);
    setScaleZ(arg0);
}

public void setScale(double[][] arg0) {
    this.scaleX = arg0[0][0];
    this.scaleY = arg0[1][1];
    this.scaleZ = arg0[2][2];
}

public void setScale(Matrix4f arg0) {
    this.scaleX = arg0.getValueAt(0, 0);
    this.scaleY = arg0.getValueAt(1, 1);
    this.scaleZ = arg0.getValueAt(2, 2);
}

public void scale(double arg0) {
    scaleX(arg0);
    scaleY(arg0);
    scaleZ(arg0);
}

public Matrix4f getScale() {
    return new Matrix4f(new double[][] {
            { getScaleX(), 0, 0, 0 },
            { 0, getScaleY(), 0, 0 },
            { 0, 0, getScaleZ(), 0 },
            { 0, 0, 0, 1 }
    });
}

public void translateX(double arg0) {
    this.translateX += arg0;
}

public void translateY(double arg0) {
    this.translateY += arg0;
}

public void translateZ(double arg0) {
    this.translateZ += arg0;
}

public Matrix4f getTranslation() {
    return new Matrix4f(new double[][] {
        { 1, 0, 0, translateX },
        { 0, 1, 0, translateY },
        { 0, 0, 1, translateZ },
        { 0, 0, 0, 1 }
    });
}

}

场景类

package com.cub.cubefront;

import com.cub.cubefront.graphics.Bitmap;
import com.cub.cubefront.input.InputHandler;
import com.cub.cubefront.math.Matrix4f;
import com.cub.cubefront.math.Vector2f;
import com.cub.cubefront.math.Vector3f;
import com.cub.cubefront.mesh.Camera;
import com.cub.cubefront.mesh.Mesh;

public class Scene extends Bitmap {

private Camera defaultCam;

public InputHandler input = new InputHandler();

public Scene() {
    super(MainEngine.getWidth(), MainEngine.getHeight());
    defaultCam = new Camera();
}

public void update() { }

public void start() { }

public void render() { }

public void render(Mesh arg0) {
    Matrix4f trans = arg0.getRotation().multiply(arg0.getScale().multiply(arg0.getTranslation()));
    for (int i = 1; i < arg0.getVerticiesCount()+1; i++) { // Depth: Manipulate x and y with z
        Vector3f v1 = trans.transform(arg0.getVertexAt(i));
        for (int n = 1; n < i; n++) {
            Vector3f v2 = trans.transform(arg0.getVertexAt(n));
            drawLine(
                new Vector2f((v1.getX()), (v1.getY())),
                new Vector2f((v2.getX()), (v2.getY()))
            );
        }
    }
}

public void clear() {
    for (int i = 0; i < pixels.length; i++) {
        pixels[i] = 0;
    }
}

public Camera getCamera() {
    return defaultCam;
}

public void setCamera(Camera defaultCam) {
    this.defaultCam = defaultCam;
}

}

Matrix4f 类

package com.cub.cubefront.math;

public class Matrix4f {

private double[][] values;

public Matrix4f() {
    values = new double[4][4];
    setValues();
}

public Matrix4f(double[][] arg0) {
    setValues(arg0);
}

private Matrix4f setValues() {
    values[0][0] = 1;  values[0][1] = 0;  values[0][2] = 0;  values[0][3] = 0;
    values[1][0] = 0;  values[1][1] = 1;  values[1][2] = 0;  values[1][3] = 0;
    values[2][0] = 0;  values[2][1] = 0;  values[2][2] = 1;  values[2][3] = 0;
    values[3][0] = 0;  values[3][1] = 0;  values[3][2] = 0;  values[3][3] = 1;
    return this;
}

public Matrix4f multiply(Matrix4f arg0) {
    double res[][] = new double[4][4];
    for (int i = 0; i < 4; i++) {
        for (int j = 0; j < 4; j++) {
            for (int k = 0; k < 4; k++) {
                res[i][j] += values[i][k] * arg0.getValueAt(k, j);
            }
        }
    }

    return new Matrix4f(res);
}

public double[][] getValues() {
    return values;
}

public double getValueAt(int arg0, int arg1) {
    return values[arg0][arg1];
}

public void setValues(double[][] arg0) {
    this.values = arg0;
}

public void setValueAt(int arg0, int arg1, double arg2) {
    values[arg0][arg1] = arg2;
}

public Vector3f transform(Vector3f arg0) {
    return new Vector3f(
        (float)(arg0.getX() * values[0][0] + arg0.getY() * values[1][0] + arg0.getZ() * values[2][0]),
        (float)(arg0.getX() * values[0][1] + arg0.getY() * values[1][1] + arg0.getZ() * values[2][1]),
        (float)(arg0.getY() * values[0][2] + arg0.getY() * values[1][2] + arg0.getZ() * values[2][2])
    );
}

}

如果您仍然不明白我的意思，请看看这些图片。

图片#1:

Still Triangle

图片#2:

Triangle Rotated 30 Degrees

你看到它是如何绕角而不是中心旋转的吗？感谢您努力提供帮助!

Answer 1

当您进行变换而没有在影响对象之前将其重置为原点时，通常会发生这种情况。请记住，矩阵顺序很重要。旋转是相对于原点进行的，因此如果您的对象不在原点上，那么它会奇怪地旋转。

将其转换为(0,0,0)后尝试旋转它。然后对三角形应用所需的平移(即平移到原点、旋转、返回到原始位置)。

希望有帮助。

编辑

一般来说，如果您想围绕固定点旋转多边形，您应该平移多边形，使所需点位于 (0,0,0) 中。然后继续旋转，最后回到原来的位置。

假设您有一个带有顶点 (1,1)、(3,1) 和 (2,3) 的三角形。如果您想围绕该三角形的中心(即(2,2))旋转，您应该:

1. 从每个顶点减去 (2,2)(使 (2,2) 作为原点)
2. 然后旋转所需的角度
3. 将 (2,2) 添加到每个顶点，返回到原始位置。

同样的原则也适用于 3 维。