use bevy::prelude::*; use bevy::math::{Mat4, Quat, Affine3A}; /// creates a conventional projection matrix from frustum planes /// /// returns a potentially off-axis projection matrix pub fn make_projection_rh_from_frustum(left: f32, right: f32, bottom: f32, top: f32, near:f32, far:f32) -> Mat4 { // based on OpenSceneGraph / glFrustum implementation let a = (right + left) / (right - left); let b: f32 = (top + bottom) / (top - bottom); let c= if far.abs() > f32::MAX { -1.0 } else { -(far + near) / (far - near)}; let d = if far.abs() > f32::MAX { -2.0 * near } else { -2.0 * far * near / (far - near) }; Mat4::from_cols( Vec4::new(2.0 * near / (right-left),0.0,0.0,0.0), Vec4::new(0.0, 2.0 *near / (top-bottom), 0.0,0.0), Vec4::new(a, b, c, -1.0), Vec4::new(0.0, 0.0, d, 0.0)) } /// creates a projection from a frustum planes with a reversed depth mapped to [0..1] pub fn make_projection_rh_from_frustum_reversed(left: f32, right: f32, bottom: f32, top: f32, z_near:f32, z_far:f32) -> Mat4 { assert!(z_near > 0.0 && z_far > 0.0); // // reversed z 0..1 projection based on https://thxforthefish.com/posts/reverse_z/ // let a = (right + left) / (right - left); let b = (top + bottom) / (top - bottom); let c = z_near / (z_far - z_near); let d = z_far * z_near / (z_far - z_near); Mat4::from_cols( Vec4::new(2.0 * z_near / (right-left), 0.0,0.0,0.0), Vec4::new(0.0, 2.0 * z_near / (top-bottom), 0.0,0.0), Vec4::new(a, b, c, -1.0), Vec4::new(0.0, 0.0, d, 0.0)) } pub fn make_projection_rh_custom(fov_y: f32, aspect_ratio: f32, z_near: f32, z_far: f32) -> Mat4 { let tan_fovy = (fov_y * 0.5).tan(); // use half angle beta let right = tan_fovy * aspect_ratio * z_near; let left = -right; let top = tan_fovy * z_near; let bottom = -top; //make_projection_rh_from_frustum(left, right, bottom, top, z_near, z_far) make_projection_rh_from_frustum_reversed(left, right, bottom, top, z_near, z_far) } pub fn create_offaxis_matrices( screen_lower_left: Vec3, screen_lower_right: Vec3, screen_upper_left: Vec3, pos_eye: Vec3, z_far: f32 ) -> (Mat4,Mat4) { // let vec_right = screen_lower_right - screen_lower_left; // vr let vec_up = screen_upper_left - screen_lower_left; // vu let frustum_left = screen_lower_left - pos_eye; // va let frustum_right = screen_lower_right - pos_eye; // vb let frustum_up = screen_upper_left - pos_eye; // vc let vec_right_normalized = vec_right.normalize(); let vec_up_normalized = vec_up.normalize(); let vec_normal = vec_right_normalized.cross(vec_up_normalized).normalize(); let dist = -frustum_left.normalize().dot(vec_normal); // println!("vec_right_normalized {}",vec_right_normalized); // println!("vec_up_normalized {}",vec_up_normalized); // println!("vec_normal {}",vec_normal); // println!("Dist {}",dist); // small offset for the near plane let min_near_distance_offset = 0.01f32; // set a minimal near distance let min_near_distance = 0.00001f32; // calculate a reasonable near distance let z_near = min_near_distance.max(dist - min_near_distance_offset); // distances let left = vec_right_normalized.dot(frustum_left) * z_near / dist; // left screen edge let right = vec_right_normalized.dot(frustum_right) * z_near / dist; // right screen edge let bottom = vec_up_normalized.dot(frustum_left) * z_near / dist; // bottom screen edge let top = vec_up_normalized.dot(frustum_up) * z_near / dist; // distance eye from screen // info!("l r b t {} {} {} {}",left,right,bottom,top); // create a view frustum let projection_matrix = make_projection_rh_from_frustum_reversed(left,right,bottom,top,z_near,z_far); let view_matrix_rotation = Mat4::from_cols( Vec4::new(vec_right_normalized.x, vec_up_normalized.x, vec_normal.x ,0.0), Vec4::new(vec_right_normalized.y, vec_up_normalized.y, vec_normal.y ,0.0), Vec4::new(vec_right_normalized.z, vec_up_normalized.z, vec_normal.z ,0.0), Vec4::W ); let rotation_quat = Quat::from_mat4(&view_matrix_rotation); // Quat::from_mat4(view_matrix_rotation); // info!("Rotation Mat {:?}",view_matrix_rotation); // info!("Viewer Rotation {:?}",rotation_quat); let view_matrix_eye = Mat4::from_cols( Vec4::X, Vec4::Y, Vec4::Z, (-pos_eye).extend(1.0) ); // create resulting view matrix (this should be much simpler using glam API) let view_matrix = view_matrix_rotation * view_matrix_eye; // return tuple of view and projection (view_matrix,projection_matrix) } #[cfg(test)] mod tests { use bevy::prelude::*; use crate::{screeninfo, projection::create_offaxis_matrices}; use super::make_projection_rh_from_frustum; #[test] fn compare_projections() { // build an on-axis frustum let fovy = 33.0_f32; let aspect_ratio = 1.6666_f32; let z_near = 1.0_f32; let z_far = 1000.0_f32; let tan_fovy = (fovy * 0.5).to_radians().tan(); // use half angle beta let right = tan_fovy * aspect_ratio * z_near; let left = -right; let top = tan_fovy * z_near; let bottom = -top; let mat_frust = make_projection_rh_from_frustum(left, right, bottom, top, z_near, z_far); println!("mat 1 {:?}",mat_frust); let mat_pers = Mat4::perspective_rh_gl(fovy.to_radians(),aspect_ratio,z_near,z_far); println!("mat 2 {:?}",mat_pers); assert!(mat_frust.abs_diff_eq(mat_pers, f32::EPSILON)); } #[test] fn create_view_matrices() { // Assumptions: Screensize 6.0m x 1.8m // Viewer is 5m away from center let screen_lower_left = Vec3::new(-3.0,-0.9,0.0); let screen_lower_right = Vec3::new(3.0,-0.9,0.0); let screen_upper_left = Vec3::new(-3.0,0.9,0.0); let eye_pos = Vec3::Z * 5.0; let z_far = 100.0_f32; let (view,projection) = create_offaxis_matrices(screen_lower_left, screen_lower_right, screen_upper_left, eye_pos, z_far); println!("View {:?}",view); println!("Projection {:?}",projection); // assert!(!view.is_nan()); // assert!(!projection.is_nan()); } }