Imj.Geo.Continuous

Continuous coordinates

data Vec2 a

Continuous 2d coordinates. We use phantom types Pos, Vel, Acc to distinguish between a position, a velocity, and an acceleration.

Constructors

Vec2

Fields

• _vec2X :: !Float
• _vec2Y :: !Float

Instances

Eq (Vec2 a)

Methods

(==) :: Vec2 a -> Vec2 a -> Bool

(/=) :: Vec2 a -> Vec2 a -> Bool

Ord (Vec2 a)

Methods

compare :: Vec2 a -> Vec2 a -> Ordering

(<) :: Vec2 a -> Vec2 a -> Bool

(<=) :: Vec2 a -> Vec2 a -> Bool

(>) :: Vec2 a -> Vec2 a -> Bool

(>=) :: Vec2 a -> Vec2 a -> Bool

max :: Vec2 a -> Vec2 a -> Vec2 a

min :: Vec2 a -> Vec2 a -> Vec2 a

Show (Vec2 a)

Methods

showsPrec :: Int -> Vec2 a -> ShowS

show :: Vec2 a -> String

showList :: [Vec2 a] -> ShowS

Conversion to / from discrete coordinates

Discrete positions are converted to continuous positions by placing them at the "pixel center", ie by applying an offset of (0.5, 0.5) in pos2vec.

Then, during the inverse transformation - in vec2pos, coordinates are just floored.

Discrete speeds are converted with speed2vec. The half-pixel convention is not applied for speeds. The inverse conversion is vec2speed.

pos2vec :: Coords Pos -> Vec2 Pos

Convert a discrete position to a continuous position.

vec2pos :: Vec2 Pos -> Coords Pos

Convert a continuous position to a discrete position.

speed2vec :: Coords Vel -> Vec2 Vel

Convert a discrete speed to a continuous speed.

vec2speed :: Vec2 Vel -> Coords Vel

Convert a continuous speed to a discrete speed.

Sampled continuous geometry

Circle

translatedFullCircle

Arguments

:: Vec2 Pos

Center

-> Float

Radius

-> Float

The angle corresponding to the first sampled point

-> Int

The total number of sampled points

-> [Vec2 Pos]

Samples a circle.

translatedFullCircleFromQuarterArc

Arguments

:: Vec2 Pos

Center

-> Float

Radius

-> Float

The angle corresponding to the first sampled point

-> Int

The total number of sampled points per quarter arc.

-> [Vec2 Pos]

Samples a circle in an optimized way, to reduce the number of sin and cos calls.

The total number of points will always be a multiple of 4.

Parabola

parabola :: Vec2 Pos -> Vec2 Vel -> Frame -> Vec2 Pos

Using equation [2] in "Constant linear acceleration in any direction":

\[ \vec r = \vec r_0 + \vec v_0*t + {1 \over 2}* \vec a*t^2 \]

\[ where \]

\[ \vec r = current\;position \]

\[ \vec r_0 = initial\;position \]

\[ \vec v_0 = initial\;velocity \]

\[ \vec a = gravity\;force \]

\[ t = time \]

Polygon extremities

polyExtremities

Arguments

:: Vec2 Pos

Center

-> Float

Radius

-> Float

Rotation angle

-> Int

Number of sides of the polygon.

-> [Vec2 Pos]

Returns the extremities of a polygon. Note that it is equal to translatedFullCircle

Vec2 utilities

sumVec2d :: Vec2 a -> Vec2 a -> Vec2 a

Sums two Vec2.

scalarProd :: Float -> Vec2 a -> Vec2 a

Multiplies a Vec2 by a scalar.

rotateByQuarters :: Vec2 Pos -> [Vec2 Pos]

Creates a list of 4 Vec2 from a single one by rotating it successively by pi/2.

Reexports

data Pos

 Phantom type : position

Instances

DiscreteDistance (Coords Pos)

 Using bresenham 2d line algorithm.

Methods

distance :: Coords Pos -> Coords Pos -> Int

distanceSuccessive :: Successive (Coords Pos) -> Int

DiscreteInterpolation (Coords Pos)

 Using bresenham 2d line algorithm.

Methods

interpolate :: Coords Pos -> Coords Pos -> Int -> Coords Pos

interpolateSuccessive :: Successive (Coords Pos) -> Int -> Coords Pos

data Vel

Phantom type : velocity

data Acc

Phantom type : acceleration