Wumpus.Basic.Geometry.Base

Base geometric types and operations.

constants

quarter_pi :: Floating u => u

half_pi :: Floating u => u

two_pi :: Floating u => u

2x2 Matrix

data Matrix2'2 u

2x2 matrix, considered to be in row-major form.

 (M2'2 a b
       c d)

Constructors

M2'2 !u !u !u !u

Instances

Functor Matrix2'2

Eq u => Eq (Matrix2'2 u)

Num u => Num (Matrix2'2 u)

Show u => Show (Matrix2'2 u)

type DMatrix2'2 = Matrix2'2 Double

identity2'2 :: Num u => Matrix2'2 u

Construct the identity 2x2 matrix:

 (M2'2 1 0 
       0 1 )

det2'2 :: Num u => Matrix2'2 u -> u

Determinant of a 2x2 matrix.

transpose2'2 :: Matrix2'2 u -> Matrix2'2 u

Transpose a 2x2 matrix.

Line

data Line u

Infinite line represented by two points.

Constructors

Line (Point2 u) (Point2 u)

Instances

(Ord u, Tolerance u) => Eq (Line u)

Show u => Show (Line u)

inclinedLine :: Floating u => Point2 u -> Radian -> Line u

inclinedLine : point * ang -> Line

Make an infinite line passing through the supplied point inclined by ang.

Line in equational form

data LineEquation u

Line in equational form, i.e. Ax + By + C = 0.

Constructors

LineEquation

Fields

line_eqn_A :: !u

line_eqn_B :: !u

line_eqn_C :: !u

Instances

Eq u => Eq (LineEquation u)

Show u => Show (LineEquation u)

type DLineEquation = LineEquation Double

lineEquation :: Num u => Point2 u -> Point2 u -> LineEquation u

lineEquation : point1 * point2 -> LineEquation

Construct a line in equational form bisecting the supplied points.

pointViaX :: Fractional u => u -> LineEquation u -> Point2 u

pointViaX : x * line_equation -> Point

Calculate the point on the line for the supplied x value.

pointViaY :: Fractional u => u -> LineEquation u -> Point2 u

pointViaY : y * line_equation -> Point

Calculate the point on the line for the supplied y value.

pointLineDistance :: Floating u => Point2 u -> LineEquation u -> u

pointLineDistance : point -> line -> Distance

Find the distance from a point to a line in equational form using this formula:

 P(u,v) 
 L: Ax + By + C = 0

 (A*u) + (B*v) + C 
 -----------------
 sqrt $ (A^2) +(B^2)

A positive distance indicates the point is above the line, negative indicates below.

Line segment

data LineSegment u

Constructors

LineSegment (Point2 u) (Point2 u)

Instances

(Ord u, Tolerance u) => Eq (LineSegment u)

(Ord u, Tolerance u) => Ord (LineSegment u)

Show u => Show (LineSegment u)

type DLineSegment = LineSegment Double

rectangleLineSegments :: Num u => u -> u -> Point2 u -> [LineSegment u]

rectangleLineSegments : half_width * half_height -> [LineSegment]

Compute the line segments of a rectangle.

polygonLineSegments :: [Point2 u] -> [LineSegment u]

polygonLineSegments : [point] -> [LineSegment]

Build the line segments of a polygon fome a list of its vertices.

Cubic Bezier curves

data BezierCurve u

A Strict cubic Bezier curve.

Constructors

BezierCurve !(Point2 u) !(Point2 u) !(Point2 u) !(Point2 u)

Instances

(Ord u, Tolerance u) => Eq (BezierCurve u)

(Ord u, Tolerance u) => Ord (BezierCurve u)

Show u => Show (BezierCurve u)

type DBezierCurve = BezierCurve Double

bezierLength :: (Floating u, Ord u, Tolerance u) => BezierCurve u -> u

bezierLength : start_point * control_1 * control_2 * end_point -> Length

Find the length of a Bezier curve. The result is an approximation, with the tolerance is 0.1 of a point. This seems good enough for drawing (potentially the tolerance could be larger still).

The result is found through repeated subdivision so the calculation is potentially costly.

subdivide :: Fractional u => BezierCurve u -> (BezierCurve u, BezierCurve u)

Curve subdivision via de Casteljau's algorithm.

subdividet :: Real u => u -> BezierCurve u -> (BezierCurve u, BezierCurve u)

subdivide with an affine weight along the line...

bezierArcPoints :: Floating u => Radian -> u -> Radian -> Point2 u -> [Point2 u]

bezierArcPoints : apex_angle * radius * inclination * center -> [Point]

 ang should be in the range 0 < ang < 360deg.

 if   0 < ang <=  90 returns 4 points
 if  90 < ang <= 180 returns 7 points
 if 180 < ang <= 270 returns 10 points
 if 270 < ang <  360 returns 13 points

bezierMinorArc :: Floating u => Radian -> u -> Radian -> Point2 u -> BezierCurve u

bezierMinorArc : apex_angle * radius * rotation * center -> BezierCurve

 ang should be in the range 0 < ang <= 90deg.

Functions

affineComb :: Real u => u -> Point2 u -> Point2 u -> Point2 u

Affine combination...

midpoint :: Fractional u => Point2 u -> Point2 u -> Point2 u

midpoint : start_point * end_point -> Midpoint

Mid-point on the line formed between the two supplied points.

lineAngle :: (Floating u, Real u) => Point2 u -> Point2 u -> Radian

lineAngle : start_point * end_point -> Angle

Calculate the counter-clockwise angle between the line formed by the two points and the horizontal plane.