2d-primitives

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2d-primitives
- Description
- Author
- Requirements
- Documentation
  - Floating points
  - Constants
  - Angles
  - Vectors
  - Bounding Boxes
  - Lines
  - Polygons
  - Bezier curves
  - Colours

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

clamp f mmin mmaxprocedure: Clamp a floating-point number to a minimum and a maximum.

sqr xprocedure: Square a number.

float-minconstant: Minimum representable floating-point number.

infinityconstant

Constants

epsilonconstant

piconstant

pi/2constant

2piconstant

-piconstant

360/2piconstant

2pi/360constant

Angles

radian->degree radiansprocedure

degree->radian degreesprocedure

flip-radian-h radiansprocedure

flip-radian-v radiansprocedure

flip-degree-h degreesprocedure

flip-degree-v degreesprocedure

Vectors

vect:create x yprocedure: Returs a new vector

vect? objprocedure

vect:x vprocedure

vect:y vprocedure

zero-vectprocedure: Constant for the zero vector.

(vect=? a b #!optional (epsilon .001)procedure: Check if two vectors are equal.

vect+ a bprocedure: Add two vectors.

vect- a #!optional bprocedure: Subtract two vectors or negate a vector.

vect* v sprocedure: Scalar multiplication.

vect:dot a bprocedure: Vector dot product.

vect:cross a bprocedure: 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.

vect:perp vprocedure: Returns a perpendicular vector. <procedure>(90 degree rotation)</procedure><br/>

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

vect:project a bprocedure: Returns the vector projection of /a/ onto /b/.

angle->vect aprocedure: Returns the unit length vector for the given angle (in radians).

vect->angle vprocedure: Returns the angular direction v is pointing in (in radians).

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

vect:unrotate a bprocedure: Inverse of vect:rotate

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

vect:length vprocedure: Returns the length of v.

vect:lerp v1 v2 tprocedure: Linearly interpolate between /a/ and /b/.

vect:normalize vprocedure: Returns a normalized copy of v.

vect:clamp v lenprocedure: Clamp v to length len.

vect:lerp-const v1 v2 distprocedure: Linearly interpolate between v1 towards v2 by distance d.

vect:dist v1 v2procedure: Returns the distance between v1 and v2.

vect:dist-squared v1 v2procedure: Returns the squared distance between v1 and v2. Faster than /(vect:distance)/ when you only need to compare distances.

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

vect:spherical-lerp a b tprocedure: Spherical linearly interpolate between /a/ and /b/.

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

Bounding Boxes

rect:create l r b tprocedure: Returs a new bounding box.

rect? objprocedure: Can also be a line.

rect:l rectprocedure

rect:r rectprocedure

rect:b rectprocedure

rect:t rectprocedure

rect:for-circle p rprocedure: Constructs a /rect/ for a circle with the given position and radius.

rect:intersects? a bprocedure: Returns true if /a/ and /b/ intersect.

rect:contains? rect otherprocedure: Returns true if /other/ lies completely within /rect/.

rect:constains-vect? rect vprocedure: Returns true if /rect/ contains /v/.

rect:merge a bprocedure: Returns a bounding box that holds both bounding boxes.

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

rect:center rectprocedure: Returns the center of a bounding box.

rect:area rectprocedure: Returns the area of the bounding box.

rect:merged-area a bprocedure: Merges /a/ and /b/ and returns the area of the merged bounding box.

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

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

rect- rect vectprocedure: Substracts a vector from a rectangle.

rect+ rect vectprocedure: Adds a vector to a rectangle.

Lines

line:create a bprocedure: Makes a line from two vectors

line? objprocedure: Can also be a rect.

Polygons

(polygon:create vects)syntax: Creates a new polygon from a list of vectors.

polygon->vects polygonprocedure: Converts a polygon to a list of vertices.

polygon:triangulate polygonprocedure: Triangulates the given polygon and returns an array of vectors.

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

polygon-convex? polygonprocedure: Return #t if the given polygon is convex.

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

polygon:convex-hull vectsprocedure: Converts any polygon to a convex polygon.

Bezier curves

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

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