Crate maths_rs Copy item path
Summary Source mat multi dimensional row-major matrix with generic mat2, mat3, mat34 and mat4 implementations
there is a mat43 type for mat34 transposes but it does not support the full functionality num base traits and operations for scalar numbers, signed numbers, integers and floats prelude export float types and all functions for qick and easy integration quat generic quaternion for varying floating point precision swizz module containing vector swizzling traits vec multi dimensional column vector with generic vec2, vec3 and vec4 implementations Classification classification for tests vs planes (behind, infront or intersects) aabb_vs_aabb returns true if the aabb defined by aabb_min1 to aabb_max1 intersects aabb_min2-aabb_max2 aabb_vs_frustum returns true if the aabb defined by aabb_pos (centre) and aabb_extent is inside the frustum defined by 6 planes packed as vec4’s .xyz = normal, .w = plane distance aabb_vs_obb returns true if the aabb defined by aabb_min to aabb_max overlaps obb defined by matrix obb, where the matrix transforms an aabb with -1 to 1 extents into an obb aabb_vs_plane returns the classification of the 3D aabb defined as aabb_min to aabb_max vs the plane defined by point on plane x and normal n aabb_vs_sphere returns ture if the aabb defined by aabb_min to aabb_max intersects the sphere (or circle) centred at s with radius r abs returns the absolute (positive) value of a acos returns the arc-cosine of v where the value v is in radians almost_identity returns soft clipping (in a cubic fashion) of x; let m be the threshold (anything above m stays unchanged), and n the value things will take when the signal is zero approx returns true if value a is approximately equal to value b within the specified epsilon eps asin returns the arc-sine of v where the value v is in radians atan returns the arc-tangent of v where the value v is in radians atan2 returns the arc-tangent of v where the value v is in radians azimuth_altitude_to_xyz returns an xyz directional unit vector converted from azimuth altitude barycentric returns the barycentric coordinate (u, v, w) of point p inside triangle t1-t2-t3 capsule_vs_capsule returns true if the capsule cp0-cp1 with radius cr0 overlaps the capsule cp2-cp3 with radius cr1 capsule_vs_plane returns the classification of a capsule defined by line c1-c2 with radius r vs a plane defined by point on plane x and normal n ceil returns the ceil’d value of a (round up to nearest integer) chebyshev_normalize returns a chebyshevnormalized unit vector of a (where the normalization projects onto the unit cube) clamp returns the value x clamped to the range of min and max closest_point_on_aabb returns the closest point on the aabb defined by aabb_min and aabb_max to point p, if the point is inside the aabb it will return p closest_point_on_cone returns the closest point to p on the cone defined by cp position, with direction cv height h and radius r closest_point_on_convex_hull returns the clostest point to p on the edge of the convex hull defined by point list ‘hull’ with clockwise winding closest_point_on_line_segment returns the closest point on the line l1-l2 to point p closest_point_on_obb returns the closest point to point p on the obb defined by mat which will transform an aabb with extents -1 to 1 into an obb closest_point_on_plane returns the closest point on the plane to point p where the plane is defined by point on plane x and normal n closest_point_on_polygon returns the clostest point to p on the edge of the polygon defined by point list poly. closest_point_on_ray returns the closest point to p on the the ray starting at r0 with diection rv closest_point_on_sphere returns the closest point from p on sphere or circle centred at s with radius r closest_point_on_triangle returns the closest point to p on the triangle defined by t1-t2-t3 cone_vs_plane return the classification of cone defined by position cp, direction cv with height h and radius at the base of r
vs the plane defined by point x and normal n convex_hull_from_points returns a convex hull wound clockwise from point cloud points convex_hull_vs_convex_hull returns true if the convex hull convex0 overlaps convex1 where convex hull is an array of vertices forming a 2D convex polygon copysign returns the value a with the same sign as second paremeter sign cos returns the cosine of v where the value v is in radians cosh returns the hyperbolic cosine of v where the value v is in radians cross returns the vector cross product of a x b, makes sense only for 3 or 7 dimensional vectors cube returns value a cubed (raised to the power 3) cubic_interpolate returns the cubic interpolation of bezier control points p1-p2-p3-p4 with percentage t cubic_pulse returns a cubic pulse (y position on a graph for x); equivalent to: smoothstep(c-w,c,x)-smoothstep(c,c+w,x) cubic_tangent returns the tangent of bezier control points p1-p2-p3-p4 with percentage t deg_to_rad returns the radian value converted from value a which is specificied in degrees dist returns scalar distance between 2 points a and b (magnitude of the vector between the 2 points) dist2 returns scalar squared distance between 2 points a and b to avoid using sqrt distance returns scalar distance between 2 points a and b (magnitude of the vector between the 2 points) distance_on_line returns the distance parameter t of point p projected along the line l1-l2, the value is not clamped to the line segment extents distance_on_ray returns the distance parameter t of point p projected along the ray r0 with direction rv, the value is not clamped to 0 or the start of the ray dot returns the vector dot product between a . b exp returns the base-e exponential function of v, which is e raised to the power v exp2 returns 2 raised to the given power v exp_impulse returns an exponential impulse (y position on a graph for x); k controls the stretching of the function exp_step returns an exponential step (y position on a graph for x); k is control parameter, n is power which gives sharper curves. exp_sustained_impulse returns an exponential sustained impulse (y position on a graph for x); control on the width of attack with k and release with f floor returns the floored value of a (round down to nearest integer) fmod returns the floating point remainder of a / b focal_length_to_fov returns field of view converted from focal length with the specified aperture_width fov_to_focal_length returns focal length converted field of view with the specified aperture_width frac returns the fractional part of value a gain returns gain (y position on a graph for x); remapping the unit interval into the unit interval by expanding the sides and compressing the center get_triangle_normal returns the normalized unit vector normal of triangle t1-t2-t3 gjk_2d returns true if the 2d convex hull convex0 overlaps with convex1 using the gjk algorithm gjk_3d returns true if the 3D convex hull convex0 overlaps with convex1 using the gjk algorithm gjk_mesh_support_function finds support vertices for gjk based on convex meshses where convex0 and convex1 are an array of vertices that form a convex hull hsv_to_rgb returns an rgb value in 0-1 range converted from hsv in 0-1 range integral_smoothstep returns the integral smoothstep of x it’s derivative is never larger than 1 length returns the scalar magnitude or length of vector a lerp returns a value interpolated between edges e0 and e1 by percentage t line_segment_vs_line_segment returns the intersection point if the line segment l1-l2 intersects with s1-s2 line_segment_vs_plane returns the intersection point of the line segment l1-l2 and plane defined by point on plane x and normal n, returns None if no intersection exists line_vs_line returns the intersection point if the infinite line l1-l2 intersects with s1-s2 line_vs_plane returns the intersection point of the infinite line defined as point on line l0 and direction lv with the plane defined by point on plane x and normal n log returns the logarithm of v in base log2 returns the binary (base-2) logarithm of v log10 returns the common (base-10) logarithm of v mad returns fused multiply add m * a + b mag returns the scalar magnitude or length of vector a mag2 returns the scalar magnitude or length of vector a squared to avoid using sqrt map_to_range remap v within in_start -> in_end range to the new range out_start -> out_end max returns the maximum of a and b min returns the minimum of a and b min_max returns the tuple (min, max) of the value a and min_max tuple (min, max) modf returns the value v broken down into a tuple (fractional, integer) parts morton_1 returns the number even bits extracted from x as set bits in the return; value 0b010101 returns 0b111 morton_2 returns the number of bits divisible by 3 in x. value 0b001001001 returns 0b111 morton_to_xy returns the x,y grid position for morten order index d morton_to_xyz returns the x,y,z grid position for morten order index d morton_xy returns the morten order index from x,y position morton_xyz returns the morten order index from x,y,z position nlerp returns a value interpolated between edges e0 and e1 by percentage t with the result being normalised normalize returns a normalized unit vector of a obb_vs_obb returns true if the aabb defined by obb0 overlaps obb1 where the obb’s are defined by a matrix and the matrix transforms an aabb with -1 to 1 extents into an obb parabola returns a parabola (y position on a graph for x); use k to control its shape pcurve returns a power curve (y position on a graph for x); this is a generalziation of the parabola perp returns the perpedicular vector of a performing anti-clockwise rotation by 90 degrees plane_distance returns the distance to the plane define by a point on the plane x and normal of the plane n plane_from_normal_and_point returns a plane placked into Vec4 in the form .xyz = plane normal, .w = plane distance (constanr) from x (point on plane) and n (planes normal) point_aabb_distance returns the distance that point p is from an aabb defined by aabb_min to aabb_max point_cone_distance returns the distance from point p to the cone defined by position cp, with height h and radius at the base of r point_convex_hull_distance returns the distance from point p to the edge of the convex hull defined by point list ‘hull’ with clockwise winding point_inside_aabb returns true if point p is inside the aabb defined by aabb_min and aabb_max point_inside_cone returns true if point p is inside cone defined by position cp facing direction cv with height h and radius r point_inside_convex_hull returns true if the point p is inside the 2D convex hull defined by point list hull with clockwise winding point_inside_frustum returns true if the point p is inside the frustum defined by 6 planes packed as vec4’s .xyz = normal, .w = plane distance point_inside_obb returns true if the point p is inside the obb defined by mat which will transform an aabb with extents -1 to 1 into an obb point_inside_polygon returns true if point p is inside the polygon defined by point list poly point_inside_sphere returns true if sphere (or cirlcle) with centre s and radius r contains point p point_inside_triangle returns true if the point p is inside the triangle defined by t1-t2-t3 point_line_segment_distance returns the distance that point p is from the line segment defined by l1-l2 point_obb_distance returns the unsigned distance from point p to the obb defined by matrix obb, where the matrix transforms a unit cube
from -1 to 1 into an obb point_plane_distance returns the distance to the plane from point p where the plane is defined by point on plane x and normal n point_polygon_distance returns the distance from point p to the edge of the polygon defined by point list ‘poly’ point_sphere_distance returns the unsigned distance from point p0 to the sphere (or 2d circle) centred at s0 with radius r point_triangle_distance returns the distance point p is from a triangle defined by t1-t2-t3 point_vs_plane returns the classification of point p vs the plane defined by point on plane x and normal n poly_impulse returns a quadratic impulse (y position on a graph for x); n is the degree of the polynomial and k controls the stretching of the function powf returns value a raised to the floating point power of value b powi returns value a raised to the integer power of value b project_to_ndc returns the 3D normalized device coordinate of point p projected by view_projection matrix, perfroming homogenous divide project_to_sc returns the 2D screen coordinate of 3D point p projected with view_projection, performing homogenous divide and viewport correction
assumes screen coordinates are vup in the y-axis y.0 = bottom y.height = top project_to_sc_vdown returns the 2D screen coordinate of 3D point p projected with view_projection, performing homogenous divide and viewport correction
coordinates are vdown in the y-axis vdown = y.0 = top y.height = bottom quad_impulse returns an quadratic impulse (y position on a graph for x); k controls the stretching of the function rad_to_deg returns the degree value converted from value a which is specificied in radians ray_vs_aabb returns the intersection point of the ray with origin r0 and direction rv with the aabb defined by aabb_min and aabb_max ray_vs_capsule returns the intersection point of ray wih origin r0 and direction rv against the capsule with line c0-c1 and radius cr ray_vs_cylinder returns true if there is an intersection between ray wih origin r0 and direction rv against the cylinder with line c0-c1 and radius cr
the intersection point is return as an Option if it exists. ray_vs_line_segment returns the intersection point if the ray with origin r0 and direction rv intersects the line segment l1-l2 ray_vs_obb returns the intersection of the 3D ray with origin r0 and direction rv with the obb defined by mat ray_vs_plane returns the intersection point of the ray defined as origin of ray r0 and direction rv with the plane defined by point on plane x and normal n ray_vs_sphere returns the intersection point of ray with origin r0 and direction rv against the sphere (or circle) centred at s0 with radius r ray_vs_triangle returns the intersection point of ray r0 and normalized direction rv with triangle t0-t1-t2 recip returns the reciprocal of value a rgb_to_hsv returns a hsv value in 0-1 range converted from rgb in 0-1 range rgba8_to_vec4 returns a vec4 of rgba in 0-1 range from a packed rgba which is inside u32 (4 bytes, 0xRRGGBBAA) rotate_2d returns the vec2 rotated anti-clockwise rotation by radian angle round returns the value a rounded to closest integer floor if a < 0.5 or ceil if a >= 0.5 rsqrt returns the reciprocal square root of value a saturate returns the saturated value of x into to the 0-1 range, this is the same as clamp(x, 0.0, 1.0) scalar_triple returns the scalar triple product of a x b x c, makes sense only for 3 dimensional vectors shortest_line_segment_between_line_and_line_segment returns the shortest line segment between 2 line segments p1-p2 and p3-p4 as an option tuple where .0 is the point on line segment 1 and .1 is the point on line segment 2 shortest_line_segment_between_line_segments returns the shortest line segment between 2 line segments p1-p2 and p3-p4 as an option tuple where .0 is the point on line segment 1 and .1 is the point on line segment 2 shortest_line_segment_between_lines returns the shortest line segment between 2 lines p1-p2 and p3-p4 as an option tuple where .0 is the point on line segment 1 and .1 is the point on line segment 2 signum returns -1 if value a is negative, 1 if positive and 0 if zero (integers) sin returns the sine of v where the value v is in radians sin_cos returns a tuple of (sin(v), cos(v)) of v where the value v is in radian sinc returns a sin curve (y position on a graph for x); can be used for some bouncing behaviors. give k different integer values to tweak the amount of bounces sinh returns the hyperbolic sine of v where the value v is in radians slerp returns a value spherically interpolated between edges e0 and e1 by percentage t smooth_start2 returns value t between the range c and d with offset b creating smooth easing at the start (t^2) smooth_start3 returns value t between the range c and d with offset b creating smooth easing at the start (t^3) smooth_start4 returns value t between the range c and d with offset b creating smooth easing at the start (t^4) smooth_start5 returns value t between the range c and d with offset b creating smooth easing at the start (t^5) smooth_stop2 returns value t between the range c and d with offset b creating smooth easing at the end of t (t^2) smooth_stop3 returns value t between the range c and d with offset b creating smooth easing at the end of t (t^3) smooth_stop4 returns value t between the range c and d with offset b creating smooth easing at the end of t (t^4) smooth_stop5 returns value t between the range c and d with offset b creating smooth easing at the end of t (t^5) smoothstep returns the hermite interpolated value between edge e0 and e1 by percentage t sphere_vs_capsule returns true if the sphere or circle at centre s1 with radius r1 intsercts capsule c0-c1 with radius cr sphere_vs_frustum returns true if the sphere with centre s and radius r is inside the frustum defined by 6 planes packed as vec4’s .xyz = normal, .w = plane distance sphere_vs_obb returns true if the sphere with centre s0 and radius r0 overlaps obb defined by matrix obb, where the matrix
transforms a unit cube with extents -1 to 1 into an obb sphere_vs_plane returns the classification of sphere defined by centre s and radius r vs the plane defined by point on plane x and normal n sphere_vs_sphere returns true if the sphere or circle at centre s1 with radius r1 intsercts s2-r2 sqr returns value a squared (raised to the power 2) sqrt returns the square root of value a step returns 1 if a > b or 0 otherwise tan returns the tangent of v where the value v is in radians tanh returns the hyperbolic tangent of v where the value v is in radians trunc truncates value a - removing the fractional part, truncating to an integer unproject_ndc returns the unprojected 3D world position of point p which is specified in normalized device coordinates unproject_sc returns the unprojected 3D world position of screen coordinate p
assumes screen coordinates are vup in the y-axis y.0 = bottom y.height = top unproject_sc_vdown returns the unprojected 3D world position of screen coordinate p
coordinates are vdown in the y-axis vdown = y.0 = top y.height = bottom vec4_to_rgba8 returns a packed u32 containing rgba8 (4 bytes, R8G8B8A8) converted from a Vec4 v of rgba in 0-1 range vector_triple returns the vector triple product of a x b x c, mainly used for 3D vectors, but with a 2D specialisation leveraging z-up xyz_to_azimuth_altitude returns (azimuth, altitude) converted from directional unit vector xyz Mat2d Mat2f Mat3d Mat3f Mat4d Mat4f Mat34d Mat34f Mat43d Mat43f Quatd Quatf Vec2d Vec2f opinionated type abbreviations Vec2i Vec2u Vec3d Vec3f Vec3i Vec3u Vec4d Vec4f Vec4i Vec4u