Question

我在两个对象描述的游戏引擎中有我的对象：位置向量：（x，y，z）;和旋转四元数：（w，a，b，c）

我现在正在寻找构建模型视图矩阵所需的数学，我有数学而不是编程背景，所以教程我找到了参考函数，我宁愿更好地理解原始计算。

它是用Java构建的，以opengl作为渲染引擎

顺便说一下，有没有人知道java中用于设置模型矩阵的方法？即：

Float [3] [3] matrix = new matrix; ModelMatrix.set（矩阵）

Answer 1

以下是来自jMonkeyEngine's Quaternion class的方法这是一个4x4矩阵结构的浮点数[16]。

public float[] toRotationMatrix(float[] result) {

        float norm = norm();
        // we explicitly test norm against one here, saving a division
        // at the cost of a test and branch.  Is it worth it?
        float s = (norm == 1f) ? 2f : (norm > 0f) ? 2f / norm : 0;

        // compute xs/ys/zs first to save 6 multiplications, since xs/ys/zs
        // will be used 2-4 times each.
        float xs = x * s;
        float ys = y * s;
        float zs = z * s;
        float xx = x * xs;
        float xy = x * ys;
        float xz = x * zs;
        float xw = w * xs;
        float yy = y * ys;
        float yz = y * zs;
        float yw = w * ys;
        float zz = z * zs;
        float zw = w * zs;

        // using s=2/norm (instead of 1/norm) saves 9 multiplications by 2 here
        result[0] = 1 - (yy + zz);
        result[1] = (xy - zw);
        result[2] = (xz + yw);
        result[4] = (xy + zw);
        result[5] = 1 - (xx + zz);
        result[6] = (yz - xw);
        result[8] = (xz - yw);
        result[9] = (yz + xw);
        result[10] = 1 - (xx + yy);

        return result;
    }

因为你要求整个模型矩阵：翻译在同一矩阵中占据位置3,7,11。编辑：查询显示我的规模是错误的。

Answer 2

这就是我使用的，q是四元数：

matrix = new float[3][3];
float x2 = q.x*q.x, y2 = q.y*q.y, z2 = q.z*q.z;
matrix[0][0] = (1-2*z2-2*y2); 
matrix[0][1] = (2*q.x*q.y+2*q.w*q.z); 
matrix[0][2] = (2*q.x*q.z-2*q.w*q.y);
matrix[1][0] = (2*q.x*q.y-2*q.w*q.z); 
matrix[1][1] = (1-2*z2-2*x2); 
matrix[1][2] = (2*q.y*q.z+2*q.w*q.x);
matrix[2][0] = (2*q.x*q.z+2*q.w*q.y); 
matrix[2][1] = (2*q.y*q.z-2*q.w*q.x); 
matrix[2][2] = (1-2*y2-2*x2);

来自Quaterion的模型视图矩阵

2 个答案: