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//! Projection matrices that are intended to be used when the base coordinate //! system (i.e. the one used by the application code) is left-handed, with the //! x-axis pointing right, y-axis pointing *up*, and z-axis pointing *into the //! screen*. use crate::mat::*; use crate::vec::*; /// Orthographic projection matrix for use with OpenGL. /// /// This matrix is meant to be used when the source coordinate space is left-handed and y-up /// and the destination space is left-handed /// and y-up, with Z (depth) clip extending from -1.0 (close) to 1.0 (far). #[inline] pub fn orthographic_gl(left: f32, right: f32, bottom: f32, top: f32, near: f32, far: f32) -> Mat4 { let rml = right - left; let rpl = right + left; let tmb = top - bottom; let tpb = top + bottom; let fmn = far - near; let fpn = far + near; Mat4::new( Vec4::new(2.0 / rml, 0.0, 0.0, 0.0), Vec4::new(0.0, 2.0 / tmb, 0.0, 0.0), Vec4::new(0.0, 0.0, 2.0 / fmn, 0.0), Vec4::new(-(rpl / rml), -(tpb / tmb), -(fpn / fmn), 1.0), ) } /// Orthographic projection matrix for use with Vulkan. /// /// This matrix is meant to be used when the source coordinate space is left-handed and y-up /// and the destination space is right-handed /// and y-down, with Z (depth) clip extending from 0.0 (close) to 1.0 (far). #[inline] pub fn orthographic_vk(left: f32, right: f32, bottom: f32, top: f32, near: f32, far: f32) -> Mat4 { let rml = right - left; let rpl = right + left; let tmb = top - bottom; let tpb = top + bottom; let fmn = far - near; Mat4::new( Vec4::new(2.0 / rml, 0.0, 0.0, 0.0), Vec4::new(0.0, -2.0 / tmb, 0.0, 0.0), Vec4::new(0.0, 0.0, 1.0 / fmn, 0.0), Vec4::new(-(rpl / rml), -(tpb / tmb), -(near / fmn), 1.0), ) } /// Orthographic projection matrix for use with DirectX. /// /// This matrix is meant to be used when the source coordinate space is left-handed and y-up /// and the destination space is left-handed /// and y-up, with Z (depth) clip extending from 0.0 (close) to 1.0 (far). #[inline] pub fn orthographic_dx(left: f32, right: f32, bottom: f32, top: f32, near: f32, far: f32) -> Mat4 { let rml = right - left; let rpl = right + left; let tmb = top - bottom; let tpb = top + bottom; let fmn = far - near; Mat4::new( Vec4::new(2.0 / rml, 0.0, 0.0, 0.0), Vec4::new(0.0, 2.0 / tmb, 0.0, 0.0), Vec4::new(0.0, 0.0, 1.0 / fmn, 0.0), Vec4::new(-(rpl / rml), -(tpb / tmb), -(near / fmn), 1.0), ) } /// Perspective projection matrix meant to be used with OpenGL. /// /// * `vertical_fov` should be provided in radians. /// * `aspect_ratio` should be the quotient `width / height`. /// /// This matrix is meant to be used when the source coordinate space is left-handed and y-up /// (the standard computer graphics coordinate space) and the destination coordinate space is /// left-handed and y-up with Z (depth) clip extending from -1.0 (close) to 1.0 (far). #[inline] pub fn perspective_gl(vertical_fov: f32, aspect_ratio: f32, z_near: f32, z_far: f32) -> Mat4 { let t = (vertical_fov / 2.0).tan(); let sy = 1.0 / t; let sx = sy / aspect_ratio; let nmf = z_near - z_far; Mat4::new( Vec4::new(sx, 0.0, 0.0, 0.0), Vec4::new(0.0, sy, 0.0, 0.0), Vec4::new(0.0, 0.0, (z_far + z_near) / nmf, 1.0), Vec4::new(0.0, 0.0, 2.0 * z_near * z_far / nmf, 0.0), ) } /// Perspective projection matrix meant to be used with DirectX. /// /// * `vertical_fov` should be provided in radians. /// * `aspect_ratio` should be the quotient `width / height`. /// /// This matrix is meant to be used when the source coordinate space is left-handed and y-up /// (the standard computer graphics coordinate space) and the destination coordinate space is /// left-handed and y-up with Z (depth) clip extending from 0.0 (close) to 1.0 (far). #[inline] pub fn perspective_dx(vertical_fov: f32, aspect_ratio: f32, z_near: f32, z_far: f32) -> Mat4 { let t = (vertical_fov / 2.0).tan(); let sy = 1.0 / t; let sx = sy / aspect_ratio; let nmf = z_near - z_far; Mat4::new( Vec4::new(sx, 0.0, 0.0, 0.0), Vec4::new(0.0, sy, 0.0, 0.0), Vec4::new(0.0, 0.0, z_far / nmf, 1.0), Vec4::new(0.0, 0.0, z_near * z_far / nmf, 0.0), ) } /// Perspective projection matrix meant to be used with Vulkan. /// /// * `vertical_fov` should be provided in radians. /// * `aspect_ratio` should be the quotient `width / height`. /// /// This matrix is meant to be used when the source coordinate space is left-handed and y-up /// (the standard computer graphics coordinate space) and the destination coordinate space is /// right-handed and y-down with Z (depth) clip extending from 0.0 (close) to 1.0 (far). #[inline] pub fn perspective_vk(vertical_fov: f32, aspect_ratio: f32, z_near: f32, z_far: f32) -> Mat4 { let t = (vertical_fov / 2.0).tan(); let sy = 1.0 / t; let sx = sy / aspect_ratio; let nmf = z_near - z_far; Mat4::new( Vec4::new(sx, 0.0, 0.0, 0.0), Vec4::new(0.0, -sy, 0.0, 0.0), Vec4::new(0.0, 0.0, z_far / nmf, 1.0), Vec4::new(0.0, 0.0, z_near * z_far / nmf, 0.0), ) } /// Perspective projection matrix with infinite z-far plane meant to be used with OpenGL. /// /// This is useful for extremely large scenes where having a far clip plane is extraneous anyway, /// as allowing it to approach infinity it eliminates several approximate numerical computations /// and so can improve z-fighting behavior. /// /// * `vertical_fov` should be provided in radians. /// * `aspect_ratio` should be the quotient `width / height`. /// /// This matrix is meant to be used when the source coordinate space is left-handed and y-up /// (the standard computer graphics coordinate space) and the destination coordinate space is /// left-handed and y-up with Z (depth) clip extending from -1.0 (close) to 1.0 (far). #[inline] pub fn perspective_infinite_z_gl(vertical_fov: f32, aspect_ratio: f32, z_near: f32) -> Mat4 { let t = (vertical_fov / 2.0).tan(); let sy = 1.0 / t; let sx = sy / aspect_ratio; Mat4::new( Vec4::new(sx, 0.0, 0.0, 0.0), Vec4::new(0.0, sy, 0.0, 0.0), Vec4::new(0.0, 0.0, -1.0, 1.0), Vec4::new(0.0, 0.0, -2.0 * z_near, 0.0), ) } /// Perspective projection matrix with infinite z-far plane meant to be used with Vulkan. /// /// This is useful for extremely large scenes where having a far clip plane is extraneous anyway, /// as allowing it to approach infinity it eliminates several approximate numerical computations /// and so can improve z-fighting behavior. /// /// * `vertical_fov` should be provided in radians. /// * `aspect_ratio` should be the quotient `width / height`. /// /// This matrix is meant to be used when the source coordinate space is left-handed and y-up /// (the standard computer graphics coordinate space) and the destination coordinate space is /// right-handed and y-down with Z (depth) clip extending from 0.0 (close) to 1.0 (far). #[inline] pub fn perspective_infinite_z_vk(vertical_fov: f32, aspect_ratio: f32, z_near: f32) -> Mat4 { let t = (vertical_fov / 2.0).tan(); let sy = 1.0 / t; let sx = sy / aspect_ratio; Mat4::new( Vec4::new(sx, 0.0, 0.0, 0.0), Vec4::new(0.0, -sy, 0.0, 0.0), Vec4::new(0.0, 0.0, -1.0, 1.0), Vec4::new(0.0, 0.0, -z_near, 0.0), ) } /// Perspective projection matrix with infinite z-far plane meant to be used with DirectX. /// /// This is useful for extremely large scenes where having a far clip plane is extraneous anyway, /// as allowing it to approach infinity it eliminates several approximate numerical computations /// and so can improve z-fighting behavior. /// /// * `vertical_fov` should be provided in radians. /// * `aspect_ratio` should be the quotient `width / height`. /// /// This matrix is meant to be used when the source coordinate space is left-handed and y-up /// (the standard computer graphics coordinate space) and the destination coordinate space is /// left-handed and y-up with Z (depth) clip extending from 0.0 (close) to 1.0 (far). #[inline] pub fn perspective_infinite_z_dx(vertical_fov: f32, aspect_ratio: f32, z_near: f32) -> Mat4 { let t = (vertical_fov / 2.0).tan(); let sy = 1.0 / t; let sx = sy / aspect_ratio; Mat4::new( Vec4::new(sx, 0.0, 0.0, 0.0), Vec4::new(0.0, sy, 0.0, 0.0), Vec4::new(0.0, 0.0, -1.0, 1.0), Vec4::new(0.0, 0.0, -z_near, 0.0), ) } /// Perspective projection matrix with reversed z-axis meant to be used with DirectX or OpenGL. /// /// Reversed-Z provides significantly better precision and therefore reduced z-fighting /// for most depth situations, especially when a floating-point depth buffer is used. You'll want to use /// a reversed depth comparison function and depth clear value when using this projection. /// /// * `vertical_fov` should be provided in radians. /// * `aspect_ratio` should be the quotient `width / height`. /// /// This matrix is meant to be used when the source coordinate space is left-handed and y-up /// (the standard computer graphics coordinate space) and the destination coordinate space is /// left-handed and y-up with Z (depth) clip extending from 0.0 (close) to 1.0 (far). /// /// **Note that in order for this to work properly with OpenGL, you'll need to use the `gl_arb_clip_control` extension /// and set the z clip from 0.0 to 1.0 rather than the default -1.0 to 1.0** #[inline] pub fn perspective_reversed_z_dx_gl( vertical_fov: f32, aspect_ratio: f32, z_near: f32, z_far: f32, ) -> Mat4 { let t = (vertical_fov / 2.0).tan(); let sy = 1.0 / t; let sx = sy / aspect_ratio; let nmf = z_near - z_far; Mat4::new( Vec4::new(sx, 0.0, 0.0, 0.0), Vec4::new(0.0, sy, 0.0, 0.0), Vec4::new(0.0, 0.0, -z_far / nmf - 1.0, 1.0), Vec4::new(0.0, 0.0, -z_near * z_far / nmf, 0.0), ) } /// Perspective projection matrix with reversed z-axis meant to be used with Vulkan. /// /// Reversed-Z provides significantly better precision and therefore reduced z-fighting /// for most depth situations, especially when a floating-point depth buffer is used. You'll want to use /// a reversed depth comparison function and depth clear value when using this projection. /// /// * `vertical_fov` should be provided in radians. /// * `aspect_ratio` should be the quotient `width / height`. /// /// This matrix is meant to be used when the source coordinate space is left-handed and y-up /// (the standard computer graphics coordinate space) and the destination coordinate space is /// right-handed and y-down with Z (depth) clip extending from 0.0 (close) to 1.0 (far). #[inline] pub fn perspective_reversed_z_vk( vertical_fov: f32, aspect_ratio: f32, z_near: f32, z_far: f32, ) -> Mat4 { let t = (vertical_fov / 2.0).tan(); let sy = 1.0 / t; let sx = sy / aspect_ratio; let nmf = z_near - z_far; Mat4::new( Vec4::new(sx, 0.0, 0.0, 0.0), Vec4::new(0.0, -sy, 0.0, 0.0), Vec4::new(0.0, 0.0, z_far / nmf, 1.0), Vec4::new(0.0, 0.0, -z_near * z_far / nmf, 0.0), ) } /// Perspective projection matrix with reversed and infinite z-axis meant to be used with OpenGL or DirectX. /// /// Reversed-Z provides significantly better precision and therefore reduced z-fighting /// for most depth situations, especially when a floating-point depth buffer is used. You'll want to use /// a reversed depth comparison function and depth clear value when using this projection. /// /// Infinte-Z is useful for extremely large scenes where having a far clip plane is extraneous anyway, /// as allowing it to approach infinity it eliminates several approximate numerical computations /// and so can improve z-fighting behavior. /// /// Combining them gives the best of both worlds for large scenes. /// /// * `vertical_fov` should be provided in radians. /// * `aspect_ratio` should be the quotient `width / height`. /// /// This matrix is meant to be used when the source coordinate space is left-handed and y-up /// (the standard computer graphics coordinate space) and the destination coordinate space is /// left-handed and y-up with Z (depth) clip extending from 0.0 (close) to 1.0 (far). /// /// **Note that in order for this to work properly with OpenGL, you'll need to use the `gl_arb_clip_control` extension /// and set the z clip from 0.0 to 1.0 rather than the default -1.0 to 1.0** #[inline] pub fn perspective_reversed_infinite_z_dx_gl( vertical_fov: f32, aspect_ratio: f32, z_near: f32, ) -> Mat4 { let t = (vertical_fov / 2.0).tan(); let sy = 1.0 / t; let sx = sy / aspect_ratio; Mat4::new( Vec4::new(sx, 0.0, 0.0, 0.0), Vec4::new(0.0, sy, 0.0, 0.0), Vec4::new(0.0, 0.0, 0.0, 1.0), Vec4::new(0.0, 0.0, z_near, 0.0), ) } /// Perspective projection matrix with reversed and infinite z-axis meant to be used with Vulkan. /// /// Reversed-Z provides significantly better precision and therefore reduced z-fighting /// for most depth situations, especially when a floating-point depth buffer is used. You'll want to use /// a reversed depth comparison function and depth clear value when using this projection. /// /// Infinte-Z is useful for extremely large scenes where having a far clip plane is extraneous anyway, /// as allowing it to approach infinity it eliminates several approximate numerical computations /// and so can improve z-fighting behavior. /// /// Combining them gives the best of both worlds for large scenes. /// /// * `vertical_fov` should be provided in radians. /// * `aspect_ratio` should be the quotient `width / height`. /// /// This matrix is meant to be used when the source coordinate space is left-handed and y-up /// (the standard computer graphics coordinate space) and the destination coordinate space is /// right-handed and y-down with Z (depth) clip extending from 0.0 (close) to 1.0 (far). #[inline] pub fn perspective_reversed_infinite_z_vk( vertical_fov: f32, aspect_ratio: f32, z_near: f32, ) -> Mat4 { let t = (vertical_fov / 2.0).tan(); let sy = 1.0 / t; let sx = sy / aspect_ratio; Mat4::new( Vec4::new(sx, 0.0, 0.0, 0.0), Vec4::new(0.0, -sy, 0.0, 0.0), Vec4::new(0.0, 0.0, 0.0, 1.0), Vec4::new(0.0, 0.0, z_near, 0.0), ) }