Wumpus.Basic.Geometry.Quadrant

Quadrants and trigonometric calculations.

** - WARNING ** - in progress.

Documentation

data Quadrant

Constructors

QUAD_NE

QUAD_NW

QUAD_SW

QUAD_SE

Instances

Enum Quadrant

Eq Quadrant

Ord Quadrant

Show Quadrant

quadrant :: Radian -> Quadrant

quadrant : ang -> Quadrant

Get the quadrant of an angle.

type RadialIntersect u = Radian -> Vec2 u

data QuadrantAlg u

A Quadrant algorithm.

Constructors

QuadrantAlg

Fields

calc_quad1 :: RadialIntersect u

calc_quad2 :: RadialIntersect u

calc_quad3 :: RadialIntersect u

calc_quad4 :: RadialIntersect u

runQuadrantAlg :: Radian -> QuadrantAlg u -> Vec2 u

hypotenuseQI :: (Real u, Floating u) => u -> u -> RadialIntersect u

triangleQI : dx * dy -> RadialIntersect

Find where a line from (0,0) with elevation ang intersects the hypotenuse a right triangle in QI (the legs of the triangle take the x and y-axes).

 ang must be in the @range 0 < ang <= 90@.

 width and height must be positive.

rectangleQI :: (Real u, Floating u) => u -> u -> Radian -> Vec2 u

rectangleQI : width * height * ang -> Vec

Find where a line from (0,0) in direction ang intersects the top or right side of a rectangle in QI (left side is the y-axis, bottom is the x-axis).

 ang must be in the @range 0 < ang <= 90 deg@.

 width and height must be positive.

hquadrilAcuteQI :: (Real u, Floating u) => u -> u -> Radian -> RadialIntersect u

hquadrilAcuteQI : dx * dy * ang -> RadialIntersect

Find where a line from (0,0) with elevation ang intersects a quadrilateral in H acute form in QI.

 ang must be in the @range 0 < ang <= 90@.

 dx (top width @bc@) and dy (height @ab) must be positive.

Horizontal acute quadrilateral (H because one of the two "sides of interest" is horizontal, acute because the angle of interest bcd is acute:

      
  b---*----c
  |       /
  |      %
  |     /
  a----d

hquadrilObtusQI :: (Real u, Floating u) => u -> u -> Radian -> RadialIntersect u

hquadrilObtusQI : dx * dy * ang -> RadialIntersect

Find where a line from (0,0) with elevation ang intersects a quadrilateral in H obtus form in QI.

 ang must be in the @range 0 < ang <= 90@.

 dx (top width @bc@) and dy (height @ab) must be positive.

H Obtus quadrilateral (H because one of the two "sides of interest" is horizontal, obtus because the angle interest bcd is obtuse:

      
  b---*----c
  |         \
  |          %
  |           \
  a------------d

rectangleQuadrantAlg :: (Real u, Floating u) => u -> u -> QuadrantAlg u

rectangleQuadrantAlg : width * height -> QuadrantAlg

Find where a radial line extended from (0,0) with the elevation ang intersects with an enclosing rectangle. The rectangle is centered at (0,0).

Internally the calculation is made in quadrant I (north east), symmetry is used to translate result to the other quadrants.

diamondQuadrantAlg :: (Real u, Floating u) => u -> u -> QuadrantAlg u

diamondQuadrantAlg : width * height -> QuadrantAlg

Find where a radial line extended from (0,0) with the elevation ang intersects with an enclosing diamond. The diamond is centered at (0,0).

Internally the calculation is made in quadrant I (north east), symmetry is used to translate result to the other quadrants.

isoscelesTriQuadrantAlg :: (Real u, Floating u) => u -> u -> QuadrantAlg u

isoscelesTriQuadrantAlg : base_width * height -> QuadrantAlg

Find where a radial line extended from (0,0) with the elevation ang intersects with an enclosing isosceles triangle.

Note the center of the triangle (0,0) is the centroid not the incenter.

Internally the calculation is made in quadrant I (north east), symmetry is used to translate result to the other quadrants.

rectRadialVector :: (Real u, Floating u) => u -> u -> Radian -> Vec2 u

rectRadialVector : half_width * half_height * ang -> Vec

Find where a radial line extended from (0,0) with the elevation ang intersects with an enclosing rectangle. The rectangle is centered at (0,0).

Internally the calculation is made in quadrant I (north east), symmetry is used to translate result to the other quadrants.

diamondRadialVector :: (Real u, Floating u) => u -> u -> Radian -> Vec2 u

diamondRadialVector : half_width * half_height * ang -> Vec

Find where a radial line extended from (0,0) with the elevation ang intersects with an enclosing diamond. The diamond is centered at (0,0).

Internally the calculation is made in quadrant I (north east), symmetry is used to translate result to the other quadrants.

triangleRadialVector :: (Real u, Floating u) => u -> u -> u -> Radian -> Vec2 u

triangleRadialVector : half_base_width * height_minor * height_minor * ang -> Vec

Find where a radial line extended from (0,0) with the elevation ang intersects with an enclosing triangle. The triangle has the centroid at (0,0), so solutions in quadrants I and II are intersections with a simple line. Intersections in quadrants III and IV can intersect either the respective side or the base.

triangleQI :: (Real u, Floating u) => u -> u -> Radian -> Vec2 u

triangleQI : width * height * ang -> Vec

Find where a line from (0,0) with elevation ang intersects the hypotenuse a right triangle in QI (the legs of the triangle take the x and y-axes).

 ang must be in the @range 0 < ang <= 90@.

 width and height must be positive.

rightTrapezoidQI :: (Real u, Floating u) => u -> u -> Radian -> Radian -> Vec2 u

rightTrapezoidQI : top_width * height * top_right_ang -> Vec

Find where a line from (0,0) with elevation ang intersects the either the lines A_B or B_D in a right trapezoid in QI.

The right trapezoid has a variable right side. Left side is the y-axis (C_A), bottom side is the x-axis (C_D), top side is parallel to the x-axis (A_B).

  A   B
  -----
  |    \
  |     \     
  -------
  C      D

  A      B
  -------
  |     /
  |    /     
  -----
  C   D

 ang must be in the range 0 < ang <= 90.

 top_width and height must be positive.

rightTrapeziumBaseWidth :: Fractional u => u -> u -> Radian -> u

rightTrapeziumBaseWidth : top_width * height * top_right_ang -> Length

Find the length of the line C_D:

  A   B
  -----
  |    \
  |     \     
  -------
  C      D

  A      B
  -------
  |     /
  |    /     
  -----
  C   D