nicheware.platform.utilities.common.graphics.line — nicheware/cljc-common 1.0.0

Functions for with mathematical straight and curved lines:

There are groups of functions and variables within line that deal with:

Function group	Functions
equations	straight-line-equation, [[bezier-qudaratic-equation]], bezier-cubic-equation
curve and line building functions	make-lerp, lerp, [[make-curve-fn-from-sample]], rasterize-bezier-quadratic, interpolate-n-points

bezier-cubic-equation clj/s

(bezier-cubic-equation start control1 control2 end)

Creates a function for computing points on a quadratic Bezier curve (from 5 control points) The returned function will accept a fraction from 0 to 1 which will return a point on the curve running from start to end, controlled by the middle two control points.

Lines are computed between:

• start -> control1 (L1)
• control1 -> control2 (L2)
• control2 -> end (L3)

t (fraction 0 to 1) will compute points on each line, resulting in T1, T2, T3

These are then used as a bezier-quadratic-equation.

• start: Start control point. N-dimensional.
• control1: Middle control point 1. N-dimensional.
• control2: Middle control point 2. N-dimensional.
• end: End control point. N-dimensional.
• returns: function which takes a single argument from 0 to 1. Returns a N-dimensional point on the curve.

bezier-quadratic-equation clj/s

(bezier-quadratic-equation start middle end)

Creates a function for computing points on a quadratic Bezier curve (from 3 control points)

The returned function will accept a fraction from 0 to 1 which will return a point on the curve running from start to end, controlled by the middle.

The middle point is used to calculate a line between the start and end point. The fraction then computes a point along each of these lines, which will be the tangent to the point on the curve. The point is the fraction of this resulting line.

• start: Start control point. N-dimensional.
• middle: Middle control point. N-dimensional.
• end: End control point. N-dimensional.
• returns: function which takes a single argument from 0 to 1. Returns a N-dimensional point on the curve.

interpolate-n-points clj/s

(interpolate-n-points interpolation-fn points)

Compute the given number of points between start and end. This will divide the curve into points + 1 sections, and gives the curve value for n points.

• interpolation-fn: Curve interpolation function which should accept t, as value form 0 to 1
• points: An integer number of points to interpolate evenly using the function.

lerp clj/s

(lerp point1 point2 fraction)

Calculates the point [x y ...] that is fraction between the two given points (of any dimension).

Does multi-dimension vector calculations, not just 2-D points.

• point1: N-dimensional point.
• point2: N-dimensional point.
• fraction is a float from 0 to 1.0.
• returns: point that ios specified fraciont between point1 and point2. Co-ords will be floats and the same dimension as the incoming points.

make-curve-fn-from-samples clj/s

(make-curve-fn-from-samples sample-points)

Creates a function to return a Y value given an X for points on a curve where the curve is represented by the given set of [x y] points

Finds the two points either size of the given X and then finds points on line between the known points.

• sample-points: Collection of points (each point is vector [x y]) which are all on a curve.
• returns: function that takes single X argument and returns the correponding Y point on the curve defined by the sample-points. Function Returns nil if given X is outside the min and max X of the sample points.

make-lerp clj/s

(make-lerp point1 point2)

Create a function that calculates the co-ordinate [x y, ...] that is fraction between the two given co-ordinates.

• fraction is a float from 0 to 1.0.
• returns: point co-ords will be floats

rasterize-bezier-quadratic clj/s

(rasterize-bezier-quadratic [x1 y1 :as start] [x2 y2 :as end] middle)

(rasterize-bezier-quadratic [x1 y1 :as start]
                            [x2 y2 :as end]
                            [x3 y3 :as middle]
                            x-start
                            x-end)

Rasterizes the bezier curve defined by the given start, end and middle control points.

Will return a value for each int x between the start x and end x.

As curve points can extend beyond the start and end point, it allows for an optional x-start and x-end to be specified for the rasterized curve, to generate a wider range of points.

These default to the start and end x.

• start: Start point defining bezier curve. [x y]
• end: End point defining bezier curve. [x y]
• middle: Middle control point defining bezier curve. [x y]
• x-start: Optional starting X for generated points. Defaults to x of start.
• x-end: Optional ending X for generated points. Defaults to x of end.
• returns: lazy sequence of points, one for each x from x-start to x-end. [x y]

straight-line-equation clj/s

(straight-line-equation [x1 y1 :as start] [x2 y2 :as end])

Given two points will create a line equation function.

• start: Vector of start point on the line. [x y]
• end: Vector of end point on the line. [x y]
• returns: function that calculates points on the line. The function will take any X and return the Y corresponding to the point on the line. The Y result will be a float