我正在努力了解如何使用“透视”投影和“正交”投影来更改算法以处理射线广播(用于MousePicking)。
当前,我有一个场景,其中包含3D对象,这些对象附加了AxisAligned边界框。
在使用透视投影渲染场景(使用glm :: perspective创建)的同时,我可以成功地使用光线投射和鼠标“拾取”场景中的不同对象。这是demonstration。
如果我渲染相同的场景,但是使用正交投影,并且将摄影机朝下放置(朝Y轴向下看,想像游戏的关卡编辑器),那么我将无法正确地从用户所在位置进行光线投射单击屏幕,以便在使用正交投影进行渲染时可以使MousePicking正常工作。这是demonstration,不有效。
我的高级算法:
auto const coords = mouse.coords();
glm::vec2 const mouse_pos{coords.x, coords.y};
glm::vec3 ray_dir, ray_start;
if (perspective) { // This "works"
auto const ar = aspect_rate;
auto const fov = field_of_view;
glm::mat4 const proj_matrix = glm::perspective(fov, ar, f.near, f.far);
auto const& target_pos = camera.target.get_position();
glm::mat4 const view_matrix = glm::lookAt(target_pos, target_pos, glm::vec3{0, -1, 0});
ray_dir = Raycast::calculate_ray_into_screen(mouse_pos, proj_matrix, view_matrix, view_rect);
ray_start = camera.world_position();
}
else if (orthographic) { // This "doesn't work"
glm::vec3 const POS = glm::vec3{50};
glm::vec3 const FORWARD = glm::vec3{0, -1, 0};
glm::vec3 const UP = glm::vec3{0, 0, -1};
// 1024, 768 with NEAR 0.001 and FAR 10000
//glm::mat4 proj_matrix = glm::ortho(0, 1024, 0, 768, 0.0001, 10000);
glm::mat4 proj_matrix = glm::ortho(0, 1024, 0, 768, 0.0001, 100);
// Look down at the scene from above
glm::mat4 view_matrix = glm::lookAt(POS, POS + FORWARD, UP);
// convert the mouse screen coordinates into world coordinates for the cube/ray test
auto const p0 = screen_to_world(mouse_pos, view_rect, proj_matrix, view_matrix, 0.0f);
auto const p1 = screen_to_world(mouse_pos, view_rect, proj_matrix, view_matrix, 1.0f);
ray_start = p0;
ray_dir = glm::normalize(p1 - p0);
}
bool const intersects = ray_intersects_cube(logger, ray_dir, ray_start,
eid, tr, cube, distances);
在透视模式下,我们将射线投射到场景中,看它是否与对象周围的立方体相交。
在正交模式下,我要从屏幕投射两条射线(一条在z = 0处,另一条在z = 1处)并在这两点之间创建一条射线。我将射线起点设置为鼠标指针所在的位置(z = 0),并使用刚刚计算出的射线方向作为相同ray_cube_intersection算法的输入。
由于MousePicking使用的是“透视”投影,而不是“正交”投影,因此:
glm::vec3
Raycast::calculate_ray_into_screen(glm::vec2 const& point, glm::mat4 const& proj,
glm::mat4 const& view, Rectangle const& view_rect)
{
// When doing mouse picking, we want our ray to be pointed "into" the screen
float constexpr Z = -1.0f;
return screen_to_world(point, view_rect, proj, view, Z);
}
bool
ray_cube_intersect(Ray const& r, Transform const& transform, Cube const& cube,
float& distance)
{
auto const& cubepos = transform.translation;
glm::vec3 const minpos = cube.min * transform.scale;
glm::vec3 const maxpos = cube.max * transform.scale;
std::array<glm::vec3, 2> const bounds{{minpos + cubepos, maxpos + cubepos}};
float txmin = (bounds[ r.sign[0]].x - r.orig.x) * r.invdir.x;
float txmax = (bounds[1 - r.sign[0]].x - r.orig.x) * r.invdir.x;
float tymin = (bounds[ r.sign[1]].y - r.orig.y) * r.invdir.y;
float tymax = (bounds[1 - r.sign[1]].y - r.orig.y) * r.invdir.y;
if ((txmin > tymax) || (tymin > txmax)) {
return false;
}
if (tymin > txmin) {
txmin = tymin;
}
if (tymax < txmax) {
txmax = tymax;
}
float tzmin = (bounds[ r.sign[2]].z - r.orig.z) * r.invdir.z;
float tzmax = (bounds[1 - r.sign[2]].z - r.orig.z) * r.invdir.z;
if ((txmin > tzmax) || (tzmin > txmax)) {
return false;
}
distance = tzmin;
return true;
}
编辑:我正在使用的数学空间转换功能:
namespace boomhs::math::space_conversions
{
inline glm::vec4
clip_to_eye(glm::vec4 const& clip, glm::mat4 const& proj_matrix, float const z)
{
auto const inv_proj = glm::inverse(proj_matrix);
glm::vec4 const eye_coords = inv_proj * clip;
return glm::vec4{eye_coords.x, eye_coords.y, z, 0.0f};
}
inline glm::vec3
eye_to_world(glm::vec4 const& eye, glm::mat4 const& view_matrix)
{
glm::mat4 const inv_view = glm::inverse(view_matrix);
glm::vec4 const ray = inv_view * eye;
glm::vec3 const ray_world = glm::vec3{ray.x, ray.y, ray.z};
return glm::normalize(ray_world);
}
inline constexpr glm::vec2
screen_to_ndc(glm::vec2 const& scoords, Rectangle const& view_rect)
{
float const x = ((2.0f * scoords.x) / view_rect.right()) - 1.0f;
float const y = ((2.0f * scoords.y) / view_rect.bottom()) - 1.0f;
auto const assert_fn = [](float const v) {
assert(v <= 1.0f);
assert(v >= -1.0f);
};
assert_fn(x);
assert_fn(y);
return glm::vec2{x, -y};
}
inline glm::vec4
ndc_to_clip(glm::vec2 const& ndc, float const z)
{
return glm::vec4{ndc.x, ndc.y, z, 1.0f};
}
inline glm::vec3
screen_to_world(glm::vec2 const& scoords, Rectangle const& view_rect, glm::mat4 const& proj_matrix,
glm::mat4 const& view_matrix, float const z)
{
glm::vec2 const ndc = screen_to_ndc(scoords, view_rect);
glm::vec4 const clip = ndc_to_clip(ndc, z);
glm::vec4 const eye = clip_to_eye(clip, proj_matrix, z);
glm::vec3 const world = eye_to_world(eye, view_matrix);
return world;
}
} // namespace boomhs::math::space_conversions
答案 0 :(得分:0)
我为此工作了几天,因为我遇到了同样的问题。 我们用来使用的非投影方法在这里也 100% 正确 - 即使使用正交投影。但是对于正交投影,从相机位置到屏幕的方向向量总是相同的。因此,在这种情况下,以相同的方式取消投影光标不会按预期工作。
您想要做的是按原样获取相机方向矢量,但为了获得光线原点,您需要根据当前鼠标在屏幕上的位置移动相机位置。
我的方法(C#,但你会明白的):
Vector3 worldUpDirection = new Vector3(0, 1, 0); // if your world is y-up
// Get mouse coordinates (2d) relative to window position:
Vector2 mousePosRelativeToWindow = GetMouseCoordsRelativeToWindow(); // (0,0) would be top left window corner
// get camera direction vector:
Vector3 camDirection = Vector3.Normalize(cameraTarget - cameraPosition);
// get x and y coordinates relative to frustum width and height.
// glOrthoWidth and glOrthoHeight are the sizeX and sizeY values
// you created your projection matrix with. If your frustum has a width of 100,
// x would become -50 when the mouse is left and +50 when the mouse is right.
float x = +(2.0f * mousePosRelativeToWindow .X / viewportWidth - 1) * (glOrthoWidth / 2);
float y = -(2.0f * mousePosRelativeToWindow .Y / viewPortHeight - 1) * (glOrthoHeight / 2);
// Now, you want to calculate the camera's local right and up vectors
// (depending on the camera's current view direction):
Vector3 cameraRight = Vector3.Normalize(Vector3.Cross(camDirection, worldUpDirection));
Vector3 cameraUp = Vector3.Normalize(Vector3.Cross(cameraRight, camDirection));
// Finally, calculate the ray origin:
Vector3 rayOrigin = cameraPosition + cameraRight * x + cameraUp * y;
Vector3 rayDirection = camDirection;
现在您有了正交投影的射线原点和射线方向。 有了这些,您可以像往常一样运行任何光线平面/体积相交。