use bevy::math::{Affine3A, Mat4, Quat}; use bevy::prelude::*; /// 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); let sx = 2.0 * z_near / (right - left); let sy = 2.0 * z_near / (top - bottom); // Mat4::from_cols( Vec4::new(sx, 0.0, 0.0, 0.0), Vec4::new(0.0, sy, 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::{projection::create_offaxis_matrices, screeninfo}; 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()); } }