## Modules§

- 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
- base traits and operations for scalar numbers, signed numbers, integers and floats
- export float types and all functions for qick and easy integration
- generic quaternion for varying floating point precision
- module containing vector swizzling traits
- multi dimensional column vector with generic vec2, vec3 and vec4 implementations

## Enums§

- classification for tests vs planes (behind, infront or intersects)

## Functions§

- returns true if the aabb defined by
`aabb_min1`

to`aabb_max1`

intersects`aabb_min2-aabb_max2`

- 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`

- 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 - 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`

- returns ture if the aabb defined by
`aabb_min`

to`aabb_max`

intersects the sphere (or circle) centred at`s`

with radius`r`

- returns the absolute (positive) value of
`a`

- returns the arc-cosine of
`v`

where the value`v`

is in radians - 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 - returns true if value
`a`

is approximately equal to value`b`

within the specified epsilon`eps`

- returns the arc-sine of
`v`

where the value`v`

is in radians - returns the arc-tangent of
`v`

where the value`v`

is in radians - returns the arc-tangent of
`v`

where the value`v`

is in radians - returns an
`xyz`

directional unit vector converted from azimuth altitude - returns the barycentric coordinate
`(u, v, w)`

of point`p`

inside triangle`t1-t2-t3`

- returns true if the capsule
`cp0-cp1`

with radius`cr0`

overlaps the capsule`cp2-cp3`

with radius`cr1`

- 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`

- returns the ceil’d value of
`a`

(round up to nearest integer) - returns a chebyshevnormalized unit vector of
`a`

(where the normalization projects onto the unit cube) - returns the value
`x`

clamped to the range of`min`

and`max`

- 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`

- returns the closest point to
`p`

on the cone defined by`cp`

position, with direction`cv`

height`h`

and radius`r`

- returns the clostest point to
`p`

on the edge of the convex hull defined by point list ‘hull’ with clockwise winding - returns the closest point on the line
`l1-l2`

to point`p`

- 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 - returns the closest point on the plane to point
`p`

where the plane is defined by point on plane`x`

and normal`n`

- returns the clostest point to
`p`

on the edge of the polygon defined by point list`poly`

. - returns the closest point to
`p`

on the the ray starting at`r0`

with diection`rv`

- returns the closest point from
`p`

on sphere or circle centred at`s`

with radius`r`

- returns the closest point to
`p`

on the triangle defined by`t1-t2-t3`

- 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`

- returns a convex hull wound clockwise from point cloud
`points`

- returns true if the convex hull
`convex0`

overlaps`convex1`

where convex hull is an array of vertices forming a 2D convex polygon - returns the value
`a`

with the same sign as second paremeter`sign`

- returns the cosine of
`v`

where the value`v`

is in radians - returns the hyperbolic cosine of
`v`

where the value`v`

is in radians - returns the vector cross product of
`a x b`

, makes sense only for 3 or 7 dimensional vectors - returns value
`a`

cubed (raised to the power 3) - returns the cubic interpolation of bezier control points
`p1-p2-p3-p4`

with percentage t - returns a cubic pulse (y position on a graph for
`x`

); equivalent to:`smoothstep(c-w,c,x)-smoothstep(c,c+w,x)`

- returns the tangent of bezier control points
`p1-p2-p3-p4`

with percentage t - returns the radian value converted from value
`a`

which is specificied in degrees - returns scalar distance between 2 points
`a`

and`b`

(magnitude of the vector between the 2 points) - returns scalar squared distance between 2 points
`a`

and`b`

to avoid using sqrt - returns scalar distance between 2 points
`a`

and`b`

(magnitude of the vector between the 2 points) - returns the distance parameter t of point
`p`

projected along the line`l1-l2`

, the value is not clamped to the line segment extents - 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 - returns the vector dot product between
`a . b`

- returns the base-e exponential function of
`v`

, which is e raised to the power`v`

- returns 2 raised to the given power
`v`

- returns an exponential impulse (y position on a graph for
`x`

);`k`

controls the stretching of the function - returns an exponential step (y position on a graph for
`x`

);`k`

is control parameter,`n`

is power which gives sharper curves. - returns an exponential sustained impulse (y position on a graph for
`x`

); control on the width of attack with`k`

and release with`f`

- returns the floored value of
`a`

(round down to nearest integer) - returns the floating point remainder of
`a / b`

- returns field of view converted from focal length with the specified aperture_width
- returns focal length converted field of view with the specified aperture_width
- returns the fractional part of value
`a`

- 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 - returns the normalized unit vector normal of triangle
`t1-t2-t3`

- returns true if the 2d convex hull
`convex0`

overlaps with`convex1`

using the gjk algorithm - returns true if the 3D convex hull
`convex0`

overlaps with`convex1`

using the gjk algorithm - finds support vertices for gjk based on convex meshses where
`convex0`

and`convex1`

are an array of vertices that form a convex hull - returns an rgb value in 0-1 range converted from
`hsv`

in 0-1 range - returns the integral smoothstep of
`x`

it’s derivative is never larger than 1 - returns the scalar magnitude or length of vector
`a`

- returns a value interpolated between edges
`e0`

and`e1`

by percentage`t`

- returns the intersection point if the line segment
`l1-l2`

intersects with`s1-s2`

- 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 - returns the intersection point if the infinite line
`l1-l2`

intersects with`s1-s2`

- 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`

- returns the logarithm of
`v`

in`base`

- returns the binary (base-2) logarithm of
`v`

- returns the common (base-10) logarithm of
`v`

- returns fused multiply add
`m * a + b`

- returns the scalar magnitude or length of vector
`a`

- returns the scalar magnitude or length of vector
`a`

squared to avoid using sqrt - remap
`v`

within`in_start`

->`in_end`

range to the new range`out_start`

->`out_end`

- returns the maximum of
`a`

and`b`

- returns the minimum of
`a`

and`b`

- returns the tuple (min, max) of the value
`a`

and`min_max`

tuple (min, max) - returns the value
`v`

broken down into a tuple (fractional, integer) parts - returns the number even bits extracted from
`x`

as set bits in the return; value`0b010101`

returns`0b111`

- returns the number of bits divisible by 3 in
`x`

. value`0b001001001`

returns`0b111`

- returns the
`x,y`

grid position for morten order index`d`

- returns the
`x,y,z`

grid position for morten order index`d`

- returns the morten order index from
`x,y`

position - returns the morten order index from
`x,y,z`

position - returns a value interpolated between edges
`e0`

and`e1`

by percentage`t`

with the result being normalised - returns a normalized unit vector of
`a`

- 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 - returns a parabola (y position on a graph for
`x`

); use`k`

to control its shape - returns a power curve (y position on a graph for
`x`

); this is a generalziation of the parabola - returns the perpedicular vector of
`a`

performing anti-clockwise rotation by 90 degrees - returns the distance to the plane define by a point on the plane
`x`

and normal of the plane`n`

- 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) - returns the distance that point
`p`

is from an aabb defined by`aabb_min`

to`aabb_max`

- returns the distance from point
`p`

to the cone defined by position`cp`

, with height`h`

and radius at the base of`r`

- returns the distance from point
`p`

to the edge of the convex hull defined by point list ‘hull’ with clockwise winding - returns true if point
`p`

is inside the aabb defined by`aabb_min`

and`aabb_max`

- returns true if point
`p`

is inside cone defined by position`cp`

facing direction`cv`

with height`h`

and radius`r`

- returns true if the point
`p`

is inside the 2D convex hull defined by point list`hull`

with clockwise winding - returns true if the point
`p`

is inside the frustum defined by 6 planes packed as vec4’s`.xyz = normal, .w = plane distance`

- 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 - returns true if point
`p`

is inside the polygon defined by point list`poly`

- returns true if sphere (or cirlcle) with centre
`s`

and radius`r`

contains point`p`

- returns true if the point
`p`

is inside the triangle defined by`t1-t2-t3`

- returns the distance that point
`p`

is from the line segment defined by`l1-l2`

- 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 - returns the distance to the plane from point
`p`

where the plane is defined by point on plane`x`

and normal`n`

- returns the distance from point
`p`

to the edge of the polygon defined by point list ‘poly’ - returns the unsigned distance from point
`p0`

to the sphere (or 2d circle) centred at`s0`

with radius`r`

- returns the distance point
`p`

is from a triangle defined by`t1-t2-t3`

- returns the classification of point
`p`

vs the plane defined by point on plane`x`

and normal`n`

- 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 - returns value
`a`

raised to the floating point power of value`b`

- returns value
`a`

raised to the integer power of value`b`

- returns the 3D normalized device coordinate of point
`p`

projected by`view_projection`

matrix, perfroming homogenous divide - 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 - 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 - returns an quadratic impulse (y position on a graph for
`x`

);`k`

controls the stretching of the function - returns the degree value converted from value
`a`

which is specificied in radians - returns the intersection point of the ray with origin
`r0`

and direction`rv`

with the aabb defined by`aabb_min`

and`aabb_max`

- returns the intersection point of ray wih origin
`r0`

and direction`rv`

against the capsule with line`c0-c1`

and radius`cr`

- 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. - returns the intersection point if the ray with origin
`r0`

and direction`rv`

intersects the line segment`l1-l2`

- returns the intersection of the 3D ray with origin
`r0`

and direction`rv`

with the obb defined by`mat`

- 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`

- returns the intersection point of ray with origin
`r0`

and direction`rv`

against the sphere (or circle) centred at`s0`

with radius`r`

- returns the intersection point of ray
`r0`

and normalized direction`rv`

with triangle`t0-t1-t2`

- returns the reciprocal of value
`a`

- returns a hsv value in 0-1 range converted from
`rgb`

in 0-1 range - returns a vec4 of rgba in 0-1 range from a packed
`rgba`

which is inside u32 (4 bytes, 0xRRGGBBAA) - returns the vec2 rotated anti-clockwise rotation by radian
`angle`

- returns the value
`a`

rounded to closest integer floor if`a < 0.5`

or ceil if`a >= 0.5`

- returns the reciprocal square root of value
`a`

- returns the saturated value of
`x`

into to the 0-1 range, this is the same as`clamp(x, 0.0, 1.0)`

- returns the scalar triple product of
`a x b x c`

, makes sense only for 3 dimensional vectors - 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 - 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 - 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 - returns -1 if value
`a`

is negative, 1 if positive and 0 if zero (integers) - returns the sine of
`v`

where the value`v`

is in radians - returns a tuple of (sin(v), cos(v)) of
`v`

where the value`v`

is in radian - 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 - returns the hyperbolic sine of v where the value v is in radians
- returns a value spherically interpolated between edges
`e0`

and`e1`

by percentage`t`

- returns value
`t`

between the range`c`

and`d`

with offset`b`

creating smooth easing at the start (t^2) - returns value
`t`

between the range`c`

and`d`

with offset`b`

creating smooth easing at the start (t^3) - returns value
`t`

between the range`c`

and`d`

with offset`b`

creating smooth easing at the start (t^4) - returns value
`t`

between the range`c`

and`d`

with offset`b`

creating smooth easing at the start (t^5) - returns value
`t`

between the range`c`

and`d`

with offset`b`

creating smooth easing at the end of t (t^2) - returns value
`t`

between the range`c`

and`d`

with offset`b`

creating smooth easing at the end of t (t^3) - returns value
`t`

between the range`c`

and`d`

with offset`b`

creating smooth easing at the end of t (t^4) - returns value
`t`

between the range`c`

and`d`

with offset`b`

creating smooth easing at the end of t (t^5) - returns the hermite interpolated value between edge
`e0`

and`e1`

by percentage`t`

- returns true if the sphere or circle at centre
`s1`

with radius`r1`

intsercts capsule`c0-c1`

with radius`cr`

- 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`

- 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 - returns the classification of sphere defined by centre
`s`

and radius`r`

vs the plane defined by point on plane`x`

and normal`n`

- returns true if the sphere or circle at centre
`s1`

with radius`r1`

intsercts`s2-r2`

- returns value
`a`

squared (raised to the power 2) - returns the square root of value
`a`

- returns 1 if
`a > b`

or 0 otherwise - returns the tangent of
`v`

where the value`v`

is in radians - returns the hyperbolic tangent of
`v`

where the value`v`

is in radians - truncates value
`a`

- removing the fractional part, truncating to an integer - returns the unprojected 3D world position of point
`p`

which is specified in normalized device coordinates - 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 - returns the unprojected 3D world position of screen coordinate
`p`

coordinates are vdown in the y-axis vdown = y.0 = top y.height = bottom - returns a packed u32 containing rgba8 (4 bytes, R8G8B8A8) converted from a Vec4
`v`

of rgba in 0-1 range - returns the vector triple product of
`a x b x c`

, mainly used for 3D vectors, but with a 2D specialisation leveraging z-up - returns (azimuth, altitude) converted from directional unit vector
`xyz`

## Type Aliases§

- opinionated type abbreviations