3.6 KiB
Spaces
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Object Space
Local object coordinates. -
World Space
(world_matrix * object_space)
The position relatively to the origin of the world (point(0,0)below).
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Eye Space
The position relatively to the placement of the camera.let view_matrix = camera_matrix.inverse(); let eye_space = view_matrix * world_space;
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Clip Space
The position inside of the Normalized Device Coordinates (NDC) cube. In perspective projection, a 3D point in a truncated pyramid frustum (eye coordinates) is mapped to the NDC cube. The range of x-coordinate from[l,r]to[-1,1], the y-coordinate from[b,t]to[-1,1]and the z-coordinate from[-n,-f]to[-1,1]. Note that the eye coordinates are defined in the right-handed coordinate system, but NDC uses the left-handed coordinate system. That is, the camera at the origin is looking along -Z axis in eye space, but it is looking along +Z axis in NDC.let clip_space = projection_matrix * eye_space;
Examples
use nalgebra as n;
let object_space = n::Vector4::new(3.0,5.0,7.0,1.0);
let object_matrix = n::Matrix4::identity().append_translation(&n::Vector3::new(10.0,0.0,0.0));
let inv_object_matrix = object_matrix.try_inverse().unwrap();
let camera_matrix = n::Matrix4::identity().append_translation(&n::Vector3::new(0.0,0.0,100.0));
let inv_view_matrix = camera_matrix;
let view_matrix = camera_matrix.try_inverse().unwrap();
let aspect = 1.0;
let fov = 90.0f32.to_radians();
let near = 0.1;
let far = 100.0;
let perspective = n::Perspective3::new(aspect,fov,near,far);
let projection_matrix = *perspective.as_matrix();
let inv_projection_matrix = perspective.inverse();
// let left = -100.0;
// let right = 100.0;
// let bottom = -100.0;
// let top = 100.0;
// let near = 0.0;
// let far = 100.0;
// let orthographic = n::Orthographic3::new(left,right,bottom,top,near,far);
// let projection_matrix = *orthographic.as_matrix();
// let inv_projection_matrix = orthographic.inverse();
let world_space = object_matrix * object_space;
let eye_space = view_matrix * world_space;
let clip_space = projection_matrix * eye_space;
let eye_space2 = inv_projection_matrix * clip_space;
let world_space2 = inv_view_matrix * eye_space2;
let object_space2 = inv_object_matrix * world_space2;
println!("---------------------------------");
println!("object_space: {:?}", object_space);
println!("world_space: {:?}", world_space);
println!("eye_space: {:?}", eye_space);
println!("clip_space: {:?}", clip_space);
println!("eye_space2: {:?}", eye_space2);
println!("world_space2: {:?}", world_space2);
println!("object_space2: {:?}", object_space2);
Sources
Images and fragments used here are parts of the following articles: