是否可以仅使用：aspectRatio、y_scale、x_scal

Question

我正在创建一个游戏，我用 aspectRatio、y_scale、x_scale 和 frustum_length 计算视图矩阵，所以我想知道是否有一种方法可以只用这些变量来计算视锥。

变量：

float aspectRatio = (float)Display.getWidth() / (float)Display.getHeight();

float y_scale = (float) ((1f / Math.tan(Math.toRadians(FOV / 2f))) * aspectRatio);

float x_scale = y_scale / aspectRatio;

float frustum_length = FAR_PLANE - NEAR_PLANE;

Answer 1

当透视投影对称时，给定（y轴）视场角FOV、纵横比aspectRatio以及到近平面（NEAR_PLANE）和远平面（FAR_PLANE）的距离，然后视锥体的8个角点在视图中空间可以计算：float aspectRatio = (float)Display.getWidth() / (float)Display.getHeight();float y_scale = 1.0f / (float)Math.tan( Math.toRadians(FOV / 2.0) );float x_scale = y_scale * aspectRatio;float near_x = NEAR_PLANE * x_scale;float near_y = NEAR_PLANE * y_scale;float far_x = FAR_PLANE * x_scale;float far_y = FAR_PLANE * y_scale;Vector3f left_bottom_near  = new Vector3f(-near_x, -near_y, FAR_PLANE);Vector3f right_bottom_near = new Vector3f( near_x, -near_y, FAR_PLANE);Vector3f left_top_near     = new Vector3f(-near_x,  near_y, FAR_PLANE);Vector3f right_top_near    = new Vector3f( near_x,  near_y, FAR_PLANE);Vector3f left_bottom_far  = new Vector3f(-far_x, -far_y, FAR_PLANE);Vector3f right_bottom_far = new Vector3f( far_x, -far_y, FAR_PLANE);Vector3f left_top_far     = new Vector3f(-far_x,  far_y, FAR_PLANE);Vector3f right_top_far    = new Vector3f( far_x,  far_y, FAR_PLANE);如果您想知道世界空间中视锥体的 8 个角点，则必须将这些点从视图空间转换到世界空间。从世界空间转换到视图空间的矩阵，就是“视图”矩阵。可以从视图空间转换到世界空间的矩阵是逆视图矩阵（invert()）。逆视图矩阵是由视图位置、视图方向和视图的向上向量定义的矩阵。Matrix4f可以设置如下：Vector3f eyePos;    // position of the view (eye position)Vector3f targetPos; // the point which is looked at Vector3f upVec;     // up vector of the viewVector3f zAxis = Vector3f.sub(eyePos, targetPos, null);zAxis.normalise();Vector3f xAxis = Vector3f.cross(upVec, zAxis, null);xAxis.normalise();Vector3f yAxis = Vector3f.cross(zAxis, upVec, null);Matrix4f inverseView = new Matrix4f();inverseView.m00 = xAxis.x;  inverseView.m01 = xAxis.y;  inverseView.m02 = xAxis.z;  inverseView.m03 = 0.0f;inverseView.m10 = yAxis.x;  inverseView.m11 = yAxis.y;  inverseView.m12 = yAxis.z;  inverseView.m13 = 0.0f;inverseView.m20 = zAxis.x;  inverseView.m21 = zAxis.y;  inverseView.m22 = zAxis.z;  inverseView.m23 = 0.0f;inverseView.m30 = eyePos.x; inverseView.m31 = eyePos.y; inverseView.m32 = eyePos.z; inverseView.m33 = 1.0f;注意，视图空间的坐标系是右手系，其中X轴指向左侧，Y轴指向上方，然后Z轴指向视图外（注意在右手系中Z 轴是 X 轴和 Y 轴的叉积）。最后角点可以通过矩阵变换：例如Vector4f left_bottom_near_v4 = new Vector4f(    left_bottom_near.x, left_bottom_near.y, left_bottom_near.z, 1.0f);Vector4f left_bottom_near_world_v4 = new Vector4f();Matrix4f.transform(Matrix4f left, left_bottom_near_v4, left_bottom_near_world_v4);Vector3f left_bottom_near_world = new Vector3f(    left_bottom_near_world_v4 .x, left_bottom_near_world_v4 .y, left_bottom_near_world_v4 .z);