如何从偏航角计算方向矢量?

时间:2014-01-20 16:37:29

标签: java opengl math lwjgl

我有一个问题,我不知道如何继续使用Java / LWJGL计算方向向量来渲染OpenGL。

我有以下系统:

  • + X出现在屏幕右侧
  • + Z进入我的屏幕
  • + Y到屏幕顶部(海拔高度)

因此我走在XZ飞机上,现在我想实施/实施WASD运动,它应该与我目前的方向有关。 (W =向摄像机前方方向,S =向后方向等)

我有一个偏航角度,其定义如下:

  • 如果直接前进0度
  • 如果向右倾斜90度
  • 180度,如果回头
  • 向左倾斜270度

现在我只想要一个代表 yaw 方向的3D矢量,我该怎么做?

我使用以下Java代码,包括答案,但似乎还有另一个错误:

@Override
protected void mouseMoved(final int dx, final int dy) {
    float yawDelta = dx / 10f;
    float pitchDelta = dy / 10f;
    yaw += yawDelta;
    pitch += pitchDelta;
    System.out.println("yaw = " + yaw);
    direction.updateZero().updateTranslate((float)Math.sin(Math.toRadians(yaw)), 0f, (float)Math.cos(Math.toRadians(yaw))).updateNormalized();
    System.out.println("direction = " + direction);
    updateView();
}

private void checkKeys() {
    if (isKeyCurrentlyDown(Keyboard.KEY_W)) {
        eye.updateTranslate(direction);
        updateView();
    }
    if (isKeyCurrentlyDown(Keyboard.KEY_S)) {
        eye.updateTranslate(direction.negated());
        updateView();
    }
    if (isKeyCurrentlyDown(Keyboard.KEY_A)) {
        eye.updateTranslate(direction.cross(Vector3f.Y.negated()));
        updateView();
    }
    if (isKeyCurrentlyDown(Keyboard.KEY_D)) {
        eye.updateTranslate(direction.cross(Vector3f.Y));
        updateView();
    }
    if (isKeyCurrentlyDown(Keyboard.KEY_Q)) {
        eye.updateTranslate(0.0f, -1.0f, 0.0f);
        updateView();
    }
    if (isKeyCurrentlyDown(Keyboard.KEY_Z)) {
        eye.updateTranslate(0.0f, 1.0f, 0.0f);
        updateView();
    }
}

private void updateView() {
    viewMatrix.identity().fpsView(eye, roll, yaw, pitch);
    Uniforms.setUniformMatrix4(UNIFORM_VIEW_MATRIX, false, viewMatrix);
}

随后

public Matrix4f fpsView(final Vector3f eye, final float rollAngle, final float yawAngle, final float pitchAngle) {
    //roll = rolling your head, Q&E
    //yaw = looking left/right, mouseY
    //pitch = looking up/down, mouseX
    float sinRoll = (float)Math.sin(Math.toRadians(rollAngle));
    float cosRoll = (float)Math.cos(Math.toRadians(rollAngle));
    float sinYaw = (float)Math.sin(Math.toRadians(yawAngle));
    float cosYaw = (float)Math.cos(Math.toRadians(yawAngle));
    float sinPitch = (float)Math.sin(Math.toRadians(pitchAngle));
    float cosPitch = (float)Math.cos(Math.toRadians(pitchAngle));

    //TODO cannot roll yet
    Vector3f xAxis = new Vector3f(
        cosYaw,
        -sinPitch * sinYaw,
        -cosPitch * sinYaw
    );
    Vector3f yAxis = new Vector3f(
        0.0f,
        cosPitch,
        -sinPitch
    );
    Vector3f zAxis = new Vector3f(
        sinYaw,
        sinPitch * cosYaw,
        cosPitch * cosYaw
    );

    return multiply(
        xAxis.getX(),               xAxis.getY(),               xAxis.getZ(),               0.0f,   //X column
        yAxis.getX(),               yAxis.getY(),               yAxis.getZ(),               0.0f,   //Y column  
        zAxis.getX(),               zAxis.getY(),               zAxis.getZ(),               0.0f,   //Z column
        0.0f,                       0.0f,                       0.0f,                       1.0f    //W column
    ).translate(eye);
}

不知何故eye.updateTranslate()无效,只是将操作数的值添加到eye坐标。我的逻辑是否存在缺陷?

2 个答案:

答案 0 :(得分:1)

y始终为0

x =罪(偏航)
z = cos(偏航)

答案 1 :(得分:1)

旋转部分比你有点复杂。

 R = yawMat.pitchMat.rollMat 

其中:

    yawMat={ { cosZ, -sinZ, 0 }, { sinZ, cosZ , 0 }, {0,0,1 } };

    pitchMat =  { { cosY , 0 , sinY }, { 0, 1 , 0 }, { -sinY, 0, cosY } };

    rollMat = { {1,0,0 }, {0,cosX,-sinX }, {0,sinX,cosX } };

三者的点积是均匀变换中3x3旋转矩阵R的组成部分。点积的顺序很重要,所以要保持一致。

Here是我的参考。

最终的4x4矩阵应该看起来像

T = {{R00,R01,R02,X},{R10,R11,R12,Y},{R20,R21,R22,Z},{0,0,0,1}}

编辑如果你想一次进行一次旋转,那么另外两个3x3矩阵会转到身份,所以你只能在偏航中旋转一次:

R = yawMat.I.I = yawMat

所以:

R = { { cosZ, -sinZ, 0 }, { sinZ, cosZ , 0 }, {0,0,1 } }

同样适用于其他人。

正如您为了构建转换矩阵而编写的那样,它应该是:

Vector3f xAxis = new Vector3f(
    cosYaw*cosPitch,
    cosYaw* sinPitch*sinRoll - sinYaw*cosRoll,
    cosYaw*sinPitch*cosRoll + sinYaw*sinRoll
);

Vector3f yAxis = new Vector3f(
    sinYaw*cosPitch,
    sinYaw*sinPitch*sinRoll + cosYaw*cosRoll,
    sinYaw*sinPitch*cosRoll - cosYaw*sinRoll
);
Vector3f zAxis = new Vector3f(
    -sinPitch,
    cosPitch*sinRoll,
    cosPitch * cosYaw
);

假设固定旋转顺序x - > y - > z后跟翻译X,Y,Z