## 2d-primitives

## TOC »

### Description

A collection of primitives and linear algebra common for 2D graphics and 2D games.

### Author

Richard van Roy (pluizer)

### Requirements

none

### Documentation

#### Floating points

`fmod``numer``denom`procedureReturns the floating-point remainder of numer/denom (rounded towards zero).

`clamp``f``mmin``mmax`procedureClamp a floating-point number to a minimum and a maximum.

`sqr``x`procedureSquare a number.

`float-min`constantMinimum representable floating-point number.

`infinity`constant

#### Constants

`epsilon`constant

`pi`constant

`pi/2`constant

`2pi`constant

`-pi`constant

`360/2pi`constant

`2pi/360`constant

#### Angles

`radian->degree``radians`procedure

`degree->radian``degrees`procedure

`flip-radian-h``radians`procedure

`flip-radian-v``radians`procedure

`flip-degree-h``degrees`procedure

`flip-degree-v``degrees`procedure

#### Vectors

`vect:create``x``y`procedureReturs a new vector

`vect?``obj`procedure

`vect:x``v`procedure

`vect:y``v`procedure

`zero-vect`procedureConstant for the zero vector.

`(vect=? a b #!optional (epsilon .001)`procedureCheck if two vectors are equal.

`vect+``a``b`procedureAdd two vectors.

`vect-``a``#!optional``b`procedureSubtract two vectors or negate a vector.

`vect*``v``s`procedureScalar multiplication.

`vect:dot``a``b`procedureVector dot product.

`vect:cross``a``b`procedure2D vector cross product analog. The cross product of 2D vectors results in a 3D vector with only a z component. This function returns the magnitude of the z value.

`vect:perp``v`procedureReturns a perpendicular vector. <procedure>(90 degree rotation)</procedure><br/>

`vect:vperp``v`procedureReturns a perpendicular vector. <procedure>(-90 degree rotation)</procedure><br/>

`vect:project``a``b`procedureReturns the vector projection of /a/ onto /b/.

`angle->vect``a`procedureReturns the unit length vector for the given angle (in radians).

`vect->angle``v`procedureReturns the angular direction v is pointing in (in radians).

`vect:rotate``a``b`procedureUses complex number multiplication to rotate /a/ by /b/. Scaling will occur if /a/ is not a unit vector.

`vect:unrotate``a``b`procedureInverse of vect:rotate

`vect:length-squared``v`procedureReturns the squared length of v. Faster than /(vect:length)/ when you only need to compare lengths.

`vect:length``v`procedureReturns the length of v.

`vect:lerp``v1``v2``t`procedureLinearly interpolate between /a/ and /b/.

`vect:normalize``v`procedureReturns a normalized copy of v.

`vect:clamp``v``len`procedureClamp v to length len.

`vect:lerp-const``v1``v2``dist`procedureLinearly interpolate between v1 towards v2 by distance d.

`vect:dist``v1``v2`procedureReturns the distance between v1 and v2.

`vect:dist-squared``v1``v2`procedureReturns the squared distance between v1 and v2. Faster than /(vect:distance)/ when you only need to compare distances.

`vect:near?``a``b``dist`procedureReturns true if the distance between v1 and v2 is less than dist.

`vect:spherical-lerp``a``b``t`procedureSpherical linearly interpolate between /a/ and /b/.

`vect:spherical-lerp-const``a``b``angle`procedureSpherical linearly interpolate between /a/ towards /b/ by no more than angle /angle/ in radians.

#### Bounding Boxes

`rect:create``l``r``b``t`procedureReturs a new bounding box.

`rect?``obj`procedureCan also be a line.

`rect:l``rect`procedure

`rect:r``rect`procedure

`rect:b``rect`procedure

`rect:t``rect`procedure

`rect:for-circle``p``r`procedureConstructs a /rect/ for a circle with the given position and radius.

`rect:intersects?``a``b`procedureReturns true if /a/ and /b/ intersect.

`rect:contains?``rect``other`procedureReturns true if /other/ lies completely within /rect/.

`rect:constains-vect?``rect``v`procedureReturns true if /rect/ contains /v/.

`rect:merge``a``b`procedureReturns a bounding box that holds both bounding boxes.

`rect:expand``rect``v`procedureReturns a bounding box that holds both /rect/ and /v/.

`rect:center``rect`procedureReturns the center of a bounding box.

`rect:area``rect`procedureReturns the area of the bounding box.

`rect:merged-area``a``b`procedureMerges /a/ and /b/ and returns the area of the merged bounding box.

`rect:segment-query``rect``a``b`procedureReturns the fraction along the segment query the bounding box is hit. Returns /infinity/ if it doesn't hit.

`rect:intersects-segment?``rect``a``b`procedureReturn true if the bounding box intersects the line segment with ends /a/ and /b/.

`rect-``rect``vect`procedureSubstracts a vector from a rectangle.

`rect+``rect``vect`procedureAdds a vector to a rectangle.

#### Lines

`line:create``a``b`procedureMakes a line from two vectors

`line?``obj`procedureCan also be a rect.

#### Polygons

`(polygon:create vects)`syntaxCreates a new polygon from a list of vectors.

`polygon->vects``polygon`procedureConverts a polygon to a list of vertices.

`polygon:triangulate``polygon`procedureTriangulates the given polygon and returns an array of vectors.

`polygon:triangulate->triangles``polygon`procedureSame as polygon-triangulate but returns a list of triangles.

`polygon-convex?``polygon`procedureReturn #t if the given polygon is convex.

`convex-hull``vects`procedureReturns the convex hull of a group of vertices in clockwise order.

`polygon:convex-hull``vects`procedureConverts any polygon to a convex polygon.

#### Bezier curves

`bezier:create``control-points``...`procedureCreates a new bezier curve with a minimum of two control-points.

`bezier:ref``bezier``n`procedureReturn the point of a bezier at position n, where 0.0 is the start of the curve and 1.0 is the end.

`bezier->vects``bezier``accuracy`procedureReturns a list of points that make of a bezier curve. A higher /accuracy/ results in a higher resolution (more points).

#### Colours

`(rgb:create r g b #!optional (a 1.0)`procedureCreates a new RGB colour

`rgb:r``rgb`procedure

`rgb:g``rgb`procedure

`rgb:b``rgb`procedure

`rgb:a``rgb`procedure

`rgb->hsv``rgb`procedureConvers a rgb colour to a hsv colour.

`(hsv:create h s v #!optional (a 1.0)`procedureCreates a new HSV colour

`hsv:h``hsv`procedure

`hsv:s``hsv`procedure

`hsv:v``hsv`procedure

`hsv:a``hsv`procedure

`hsv->rgb``hsv`procedureConverts a hsv colour to a rgb colour.