实现六自由度滚动的几个问题

Question

我使用的相机有偏航、俯仰和滚动。当偏航==0时，相机向下看-z轴（偏航==90是正x），当俯仰==270时，相机向上看（俯仰==0是直视），当滚动==180时，相机倒置。

相机的偏航、俯仰和滚动值永远不会小于零或大于360（当任何值接近0或360时，当它通过该量时，它会自动移动到“另一侧”）。

我已经实现了3DoF，它运行得很好；然而，当我实现6DoF时，在滚动大约为90或270之前，一切似乎都在工作，然后向上和向右的向量发生奇怪的事情（向前似乎总是工作的，因为滚动围绕该轴旋转？）

我渲染的场景只是一堆块（在minecraft风格的块中），我总是能够向前/向后移动，并使用前向向量来瞄准一个块，这样我就知道前向向量已经完成。

这是我的initGL：

public void initGL() {
    GL11.glEnable(GL11.GL_TEXTURE_2D);
    GL11.glShadeModel(GL11.GL_SMOOTH);
    GL11.glClearColor(0.0f, 0.0f, 0.0f, 0.0f);
    GL11.glClearDepth(1.0);
    GL11.glEnable(GL11.GL_DEPTH_TEST);
    GL11.glDepthFunc(GL11.GL_LEQUAL);

    GL11.glMatrixMode(GL11.GL_PROJECTION);
    GL11.glLoadIdentity();

    GLU.gluPerspective(fov, ((float) Display.getWidth()) / ((float) Display.getHeight() != 0 ? Display.getHeight() : 1), 0.1f, 100.0f);//fov is 45.0f

    GL11.glMatrixMode(GL11.GL_MODELVIEW);
    GL11.glHint(GL11.GL_PERSPECTIVE_CORRECTION_HINT, GL11.GL_NICEST);
}

这里是我旋转并转换到相机视图的地方：

public final void lookThrough() {
    GL11.glRotatef(this.roll, 0.0f, 0.0f, 1.0f);
    GL11.glRotatef(this.pitch, 1.0f, 0.0f, 0.0f);
    GL11.glRotatef(this.yaw, 0.0f, 1.0f, 0.0f);
    GL11.glTranslatef(-this.position.x, -this.position.y, -this.position.z);
}

以下是我的六自由度计算：

public static final double  zeroRad         = Math.toRadians(0);
public static final double  ninetyRad       = Math.toRadians(90);
public static final double  oneEightyRad    = Math.toRadians(180);
public static final double  twoSeventyRad   = Math.toRadians(270);

public static final strictfp void updateLookVectorsIn6DoF(Vector3f yawPitchAndRoll, Vector3f forward, Vector3f up, Vector3f right) {
    final double yaw = Math.toRadians(yawPitchAndRoll.getX());
    final double pitch = Math.toRadians(yawPitchAndRoll.getY());
    final double roll = Math.toRadians(yawPitchAndRoll.getZ());

    final float sinYaw = ((float) Math.sin(yaw));
    final float cosYaw = ((float) Math.cos(yaw));

    final float sinYaw90 = ((float) Math.sin(yaw + ninetyRad));
    //final float sinYaw180 = ((float) Math.sin(yaw + oneEightyRad));
    final float cosYaw270 = ((float) Math.cos(yaw - ninetyRad));

    final float sinRoll = ((float) Math.sin(roll));
    final float cosRoll = ((float) Math.cos(roll));
    //final float sinRoll180 = ((float) Math.sin(roll + oneEightyRad));

    final float cosPitch90 = ((float) Math.cos(pitch + ninetyRad));
    //final float cosPitch270 = ((float) Math.cos(pitch + twoSeventyRad));
    final float sinPitch90 = ((float) Math.sin(pitch + ninetyRad));
    final float sinPitch270 = ((float) Math.sin(pitch - ninetyRad));

    //Forward:(No roll because roll goes around the Z axis and forward movement is in that axis.)
    float x = sinYaw * ((float) Math.cos(pitch));
    float y = -((float) Math.sin(pitch));
    float z = cosYaw * ((float) Math.cos(pitch - oneEightyRad));
    forward.set(x, y, z);

    //cos(90) = 0, cos(180) = -1, cos(270) = 0, cos(0) = 1
    //sin(90) = 1, sin(180) = 0, sin(270) = -1, sin(0) = 0

    //Up: Strange things occur when roll is near 90 or 270 and yaw is near 0 or 180
    x = -(sinYaw * cosPitch90) * cosRoll - (sinRoll * sinYaw90);
    y = -sinPitch270 * cosRoll;
    z = (cosYaw * cosPitch90) * cosRoll + (sinRoll * cosYaw270);
    up.set(x, y, z);
    //Right: Strange things occur when roll is near 90 or 270 and pitch is near 90 or 270
    x = (cosRoll * sinYaw90) - (sinRoll * (sinYaw * cosPitch90));
    y = 0 - (sinRoll * sinPitch90);//This axis works fine
    z = (cosRoll * cosYaw270) + (sinRoll * (sinYaw * cosPitch90));
    right.set(x, y, z);
}

我确实在这里发现了一个非常类似的问题，但它使用了矩阵和四元数，我不想这样做，除非我绝对必须这样做（我小心地尝试以正确的顺序乘以横摇和横摇）：LWJGL-在使用四元数和平移矩阵的六自由度相机中实现“滚动”的问题

Answer 1

所以我终于掌握了cos和sin的含义（但不要让我教它），并且能够让它发挥作用！

以下是经过改进的新代码：

public static final double  zeroRad         = Math.toRadians(0);
public static final double  ninetyRad       = Math.toRadians(90);
public static final double  oneEightyRad    = Math.toRadians(180);
public static final double  twoSeventyRad   = Math.toRadians(270);

public static final strictfp void updateLookVectorsIn6DoF(Vector3f yawPitchAndRoll, Vector3f forward, Vector3f up, Vector3f right) {
    final double yaw = Math.toRadians(yawPitchAndRoll.getX());
    final double pitch = Math.toRadians(yawPitchAndRoll.getY());
    final double roll = Math.toRadians(yawPitchAndRoll.getZ());

    final float sinYaw = ((float) Math.sin(yaw));
    final float cosYaw = ((float) Math.cos(yaw));

    final float sinYaw90 = ((float) Math.sin(yaw + ninetyRad));
    final float sinYaw270 = ((float) Math.sin(yaw - ninetyRad));//+ twoSeventyRad));
    final float cosYaw90 = ((float) Math.cos(yaw + ninetyRad));
    final float cosYaw180 = ((float) Math.cos(yaw + oneEightyRad));
    final float cosYaw270 = ((float) Math.cos(yaw - ninetyRad));//+ twoSeventyRad));

    final float sinRoll = ((float) Math.sin(roll));
    final float cosRoll = ((float) Math.cos(roll));
    final float cosRoll180 = ((float) Math.cos(roll + oneEightyRad));

    final float cosPitch90 = ((float) Math.cos(pitch + ninetyRad));
    final float sinPitch90 = ((float) Math.sin(pitch + ninetyRad));
    final float sinPitch270 = ((float) Math.sin(pitch - ninetyRad));

    //Forward:(No roll because roll goes around the Z axis and forward movement is in that axis.)
    float x = sinYaw * ((float) Math.cos(pitch));
    float y = -((float) Math.sin(pitch));
    float z = cosYaw * ((float) Math.cos(pitch - oneEightyRad));
    forward.set(x, y, z);

    //Multiply in this order: roll, pitch, yaw
    //cos(90) = 0, cos(180) = -1, cos(270) = 0, cos(0) = 1
    //sin(90) = 1, sin(180) = 0, sin(270) = -1, sin(0) = 0

    //hmm... gimbal lock, eh? No!

    //Up://
    x = (cosRoll180 * cosPitch90 * sinYaw) - (sinRoll * cosYaw180);
    y = -sinPitch270 * cosRoll;
    z = (cosRoll * cosPitch90 * cosYaw) + (sinRoll * sinYaw);
    up.set(x, y, z);
    //Right:
    x = (cosRoll * sinYaw90) - (sinRoll * cosPitch90 * cosYaw90);
    y = 0 - (sinRoll * sinPitch90);//This axis works fine
    z = (cosRoll * cosYaw270) + (sinRoll * cosPitch90 * sinYaw270);
    right.set(x, y, z);
}