1. 2d-primitives
    1. Description
    2. Author
    3. Requirements
    4. Documentation
      1. Floating points
      2. Constants
      3. Angles
      4. Vectors
      5. Bounding Boxes
      6. Lines
      7. Polygons
      8. Bezier curves
      9. Colours


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


Richard van Roy (pluizer)




Floating points

[procedure] (fmod numer denom)

Returns the floating-point remainder of numer/denom (rounded towards zero).

[procedure] (clamp f mmin mmax)

Clamp a floating-point number to a minimum and a maximum.

[procedure] (sqr x)

Square a number.

[constant] (float-min)

Minimum representable floating-point number.

[constant] infinity


[constant] epsilon
[constant] pi
[constant] pi/2
[constant] 2pi
[constant] -pi
[constant] 360/2pi
[constant] 2pi/360


[procedure] (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] (vect:create x y)

Returs a new vector

[procedure] (vect? obj)
[procedure] (vect:x v)
[procedure] (vect:y v)
[procedure] (zero-vect)

Constant for the zero vector.

[procedure] (vect=? a b #!optional (epsilon .001)

Check if two vectors are equal.

[procedure] (vect+ a b)

Add two vectors.

[procedure] (vect- a #!optional b)

Subtract two vectors or negate a vector.

[procedure] (vect* v s)

Scalar multiplication.

[procedure] (vect:dot a b)

Vector dot product.

[procedure] (vect:cross a b)

2D 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.

[procedure] (vect:perp v)

Returns a perpendicular vector. <procedure>(90 degree rotation)</procedure><br/>

[procedure] (vect:vperp v)

Returns a perpendicular vector. <procedure>(-90 degree rotation)</procedure><br/>

[procedure] (vect:project a b)

Returns the vector projection of /a/ onto /b/.

[procedure] (angle->vect a)

Returns the unit length vector for the given angle (in radians).

[procedure] (vect->angle v)

Returns the angular direction v is pointing in (in radians).

[procedure] (vect:rotate a b)

Uses complex number multiplication to rotate /a/ by /b/. Scaling will occur if /a/ is not a unit vector.

[procedure] (vect:unrotate a b)

Inverse of vect:rotate

[procedure] (vect:length-squared v)

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

[procedure] (vect:length v)

Returns the length of v.

[procedure] (vect:lerp v1 v2 t)

Linearly interpolate between /a/ and /b/.

[procedure] (vect:normalize v)

Returns a normalized copy of v.

[procedure] (vect:clamp v len)

Clamp v to length len.

[procedure] (vect:lerp-const v1 v2 dist)

Linearly interpolate between v1 towards v2 by distance d.

[procedure] (vect:dist v1 v2)

Returns the distance between v1 and v2.

[procedure] (vect:dist-squared v1 v2)

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

[procedure] (vect:near? a b dist)

Returns true if the distance between v1 and v2 is less than dist.

[procedure] (vect:spherical-lerp a b t)

Spherical linearly interpolate between /a/ and /b/.

[procedure] (vect:spherical-lerp-const a b angle)

Spherical linearly interpolate between /a/ towards /b/ by no more than angle /angle/ in radians.

Bounding Boxes

[procedure] (rect:create l r b t)

Returs a new bounding box.

[procedure] (rect? obj)

Can also be a line.

[procedure] (rect:l rect)
[procedure] (rect:r rect)
[procedure] (rect:b rect)
[procedure] (rect:t rect)
[procedure] (rect:for-circle p r)

Constructs a /rect/ for a circle with the given position and radius.

[procedure] (rect:intersects? a b)

Returns true if /a/ and /b/ intersect.

[procedure] (rect:contains? rect other)

Returns true if /other/ lies completely within /rect/.

[procedure] (rect:constains-vect? rect v)

Returns true if /rect/ contains /v/.

[procedure] (rect:merge a b)

Returns a bounding box that holds both bounding boxes.

[procedure] (rect:expand rect v)

Returns a bounding box that holds both /rect/ and /v/.

[procedure] (rect:center rect)

Returns the center of a bounding box.

[procedure] (rect:area rect)

Returns the area of the bounding box.

[procedure] (rect:merged-area a b)

Merges /a/ and /b/ and returns the area of the merged bounding box.

[procedure] (rect:segment-query rect a b)

Returns the fraction along the segment query the bounding box is hit. Returns /infinity/ if it doesn't hit.

[procedure] (rect:intersects-segment? rect a b)

Return true if the bounding box intersects the line segment with ends /a/ and /b/.

[procedure] (rect- rect vect)

Substracts a vector from a rectangle.

[procedure] (rect+ rect vect)

Adds a vector to a rectangle.


[procedure] (line:create a b)

Makes a line from two vectors

[procedure] (line? obj)

Can also be a rect.


[syntax] (polygon:create vects)

Creates a new polygon from a list of vectors.

[procedure] (polygon->vects polygon)

Converts a polygon to a list of vertices.

[procedure] (polygon:triangulate polygon)

Triangulates the given polygon and returns an array of vectors.

[procedure] (polygon:triangulate->triangles polygon)

Same as polygon-triangulate but returns a list of triangles.

[procedure] (polygon-convex? polygon)

Return #t if the given polygon is convex.

[procedure] (convex-hull vects)

Returns the convex hull of a group of vertices in clockwise order.

[procedure] (polygon:convex-hull vects)

Converts any polygon to a convex polygon.

Bezier curves

[procedure] (bezier:create control-points ...)

Creates a new bezier curve with a minimum of two control-points.

[procedure] (bezier:ref bezier n)

Return the point of a bezier at position n, where 0.0 is the start of the curve and 1.0 is the end.

[procedure] (bezier->vects bezier accuracy)

Returns a list of points that make of a bezier curve. A higher /accuracy/ results in a higher resolution (more points).


[procedure] (rgb:create r g b #!optional (a 1.0)

Creates a new RGB colour

[procedure] (rgb:r rgb)
[procedure] (rgb:g rgb)
[procedure] (rgb:b rgb)
[procedure] (rgb:a rgb)
[procedure] (rgb->hsv rgb)

Convers a rgb colour to a hsv colour.

[procedure] (hsv:create h s v #!optional (a 1.0)

Creates a new HSV colour

[procedure] (hsv:h hsv)
[procedure] (hsv:s hsv)
[procedure] (hsv:v hsv)
[procedure] (hsv:a hsv)
[procedure] (hsv->rgb hsv)

Converts a hsv colour to a rgb colour.