vec

package module
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 Go to latest Published: Jun 16, 2016 License: Apache-2.0 Imports: 2 Imported by: 2

README

vec

Simple 2D vector math.

Documentation

Overview

Package vec is a simplistic, non-optimised 2D vector math library and some routines for segment intersections and graphs in the plane.

It has two basic types, F2 and I2, representing points in the plane. The components of F2 are float64, and the components of I2 are int. Functions for I2 use int operations and avoid division where possible, though sometimes it is necessary to cast into int64 to avoid overflow.

Index

Constants

View Source 
const (
	Left = Direction(iota)
	Right
	Up
	Down
)

Direction values.

View Source 
const Epsilon = 0.0000000001

Epsilon is a small quantity used for floating point comparisons. TODO: do it a better way.

Variables

This section is empty.

Functions

func Abs 

func Abs(x int) int

Abs is the absolute value of x.

func CellsTouchingSegment 

func CellsTouchingSegment(cellSize, start, end I2, touch func(cell I2) bool) bool

CellsTouchingSegment calls touch for every rectangular cell that the line segment (start-end) overlaps, stopping at end or when touch returns false.

func Length 

func Length(u, v I2) float64

Length returns the length of u-v.

func SegmentIntersect 

func SegmentIntersect(p, q, a, b F2) (float64, bool)

SegmentIntersect tests for the intersection of the line segments p-q, a-b; if there is an intersection it returns how far along a-b the intersection occurs.

func Sgn 

func Sgn(x int) int

Sgn is the sign of X (-1, 0, or 1).

func SignedArea2 

func SignedArea2(a, b, c I2) int64

SignedArea2 returns double the signed area of the triangle abc.

Types

type Direction 

type Direction int

One of the four cardinal directions.

type Edge 

type Edge struct {
	U, V I2
}

Edge describes an edge between two I2 vertices.

func (Edge) Length 

func (e Edge) Length() float64

Length is the length of the edge.

func (Edge) Reverse 

func (e Edge) Reverse() Edge

Reverse is the edge flipped (V->U).

type F2 

type F2 struct{ X, Y float64 }

F2 is a tuple of float64 numbers, (X,Y).

func LineIntersect 

func LineIntersect(p, q, a, b F2) (F2, bool)

LineIntersect finds the intersection of the lines (infinite) through p,q and a,b, or returns false if they are parallel.

func NewF2 

func NewF2(x, y float64) F2

NewF2 is a convenience function for creating an F2.

func Unit 

func Unit(t float64) F2

Unit returns the unit vector at angle t.

func (F2) Add 

func (v F2) Add(w F2) F2

Add returns v + w.

func (F2) Arg 

func (v F2) Arg() float64

Arg returns the angle between the X-axis and the vector.

func (F2) C 

func (v F2) C() (float64, float64)

C returns the components of v (X,Y).

func (F2) Cmul 

func (v F2) Cmul(w F2) F2

Cmul returns the complex product v * w, where the X components are treated as real and the Y components as imaginary.

func (F2) Dir 

func (v F2) Dir() Direction

Dir returns the general direction of v (Up, Down, Left, Right).

func (F2) Div 

func (v F2) Div(k float64) F2

Div returns the componentwise division by k.

func (F2) Dot 

func (v F2) Dot(w F2) float64

Dot returns the dot product, v dot w.

func (F2) I2 

func (v F2) I2() I2

I2 rounds this F2 to an I2, which will generally result in loss of precision.

func (F2) InRect 

func (v F2) InRect(x0, y0, x1, y1 float64) bool

InRect tests if v is in the rectangle with topleft corner (x0, y0) and bottomright corner (x1, y1).

func (F2) Mul 

func (v F2) Mul(k float64) F2

Mul returns the scalar product k * v.

func (F2) Norm 

func (v F2) Norm() float64

Norm returns the length of v (the square root of v dot v).

func (F2) Normal 

func (v F2) Normal() F2

Normal returns a vector perpendicular to v of the same length.

func (F2) Rot 

func (v F2) Rot(t float64) F2

Rot rotates the vector by the angle t.

func (F2) RotAbout 

func (v F2) RotAbout(t float64, b F2) F2

RotAbout rotates the vector by the angle t around the vector b.

func (F2) Sub 

func (v F2) Sub(w F2) F2

Sub returns v - w.

func (F2) Unit 

func (v F2) Unit() F2

Unit returns the unit vector pointing in the same direction as v.

type Graph 

type Graph struct {
	V VertexSet        // vertices
	E map[I2]VertexSet // edges; E[u] = {v: u-v is an edge}
}

Graph is an adjacency-set implementation of a graph.

func NewGraph 

func NewGraph() *Graph

NewGraph creates a new empty *Graph.

func (*Graph) AddEdge 

func (g *Graph) AddEdge(u, v I2)

AddEdge adds the edge u-v to the graph.

func (*Graph) AllEdges 

func (g *Graph) AllEdges(f func(I2, I2) bool) bool

AllEdges runs a function for every edge.

func (*Graph) AllEdgesFacing 

func (g *Graph) AllEdgesFacing(p I2, f func(I2, I2) bool) bool

AllEdgesFacing calls f for every edge that is somewhat facing p.

func (*Graph) Blocks 

func (g *Graph) Blocks(start, end I2) bool

Blocks determines if the graph intersects the straight line segment start-end. Only edges facing start are considered.

func (*Graph) Edges 

func (g *Graph) Edges() (edges []Edge)

Edges returns all the edges as a slice.

func (*Graph) FullyBlocks 

func (g *Graph) FullyBlocks(start, end I2) bool

FullyBlocks determines if the graph intersects the straight line segment start-end, including back-facing edges.

func (*Graph) NearestBlock 

func (g *Graph) NearestBlock(start, end I2) (I2, bool)

NearestBlock returns the intersection with the graph nearest to start.

func (*Graph) NearestPoint 

func (g *Graph) NearestPoint(p I2) (e Edge, q I2)

NearestPoint finds the edge, and closest point along that edge, to the query point.

func (*Graph) NumEdges 

func (g *Graph) NumEdges() (n int)

NumEdges counts the number of edges.

type I2 

type I2 struct{ X, Y int }

I2 is a pair of integers, (X,Y).

func Div 

func Div(n, d int) I2

Div returns (n%d, n/d) as an I2.

func FindPath 

func FindPath(obstacles, paths *Graph, start, end I2, limits Rect) ([]I2, error)

FindPath finds a path from start to end, even if start and end are not vertices. The path will only use vertices contained in the limits Rect.

func LineIntersectI 

func LineIntersectI(p, q, a, b I2) (I2, bool)

LineIntersectI finds the intersection of the lines (infinite) through p,q and a,b, or returns false if they are parallel.

func LineNearestPoint 

func LineNearestPoint(u, v, p I2) (I2, int64)

LineNearestPoint locates the point on the line passing through uv that is closest to p, and returns the point and the square of the distance.

func NewI2 

func NewI2(x, y int) I2

NewI2 is a convenience function for creating an I2.

func RectRange 

func RectRange(ul, dr I2) []I2

RectRange makes a list of integer points contained in the Cartesian product [ul.X, dr.X) * [ul.Y, dr.Y).

func SegmentIntersectI 

func SegmentIntersectI(p, q, a, b I2) (I2, bool)

SegmentIntersectI tests for the intersection of the line segments p-q, a-b. If there is an intersection an approximation of the point of intersection will be returned.

func SegmentNearestPoint 

func SegmentNearestPoint(u, v, p I2) (I2, int64)

SegmentNearestPoint locates the point on the line segment uv that is closest to p, and returns the point and the square of the distance.

func (I2) Add 

func (v I2) Add(w I2) I2

Add returns v + w.

func (I2) Area 

func (v I2) Area() int

Area returns the product of X and Y.

func (I2) C 

func (v I2) C() (int, int)

C returns the components of v (X,Y).

func (I2) C64 

func (v I2) C64() (int64, int64)

C64 returns the components of v (X,Y) as int64s.

func (I2) ClampHi 

func (v I2) ClampHi(e I2) I2

ClampHi returns v, but with components clamped above by components of e.

func (I2) ClampLo 

func (v I2) ClampLo(e I2) I2

ClampLo returns v, but with components clamped below by components of e.

func (I2) Cmul 

func (v I2) Cmul(w I2) I2

Cmul returns the complex product v * w, where the X components are treated as real and the Y components as imaginary.

func (I2) Div 

func (v I2) Div(k int) I2

Div integer-divides both components by k.

func (I2) Dot 

func (v I2) Dot(w I2) int64

Dot returns the dot product, v dot w.

func (I2) EDiv 

func (v I2) EDiv(w I2) I2

EDiv returns the element-wise quotient of v and w.

func (I2) EMul 

func (v I2) EMul(w I2) I2

EMul returns the element-wise product of v and w.

func (I2) F2 

func (v I2) F2() F2

F2 casts this I2 to an F2, which may potentially cause loss of precision.

func (I2) InRect 

func (v I2) InRect(ul, dr I2) bool

InRect tests if v is in the rectangle ul-dr.

func (I2) Mod 

func (v I2) Mod(k int) I2

Mod returns the remainder of both components divided by k.

func (I2) Mul 

func (v I2) Mul(k int) I2

Mul returns the scalar product k * v.

func (I2) MulDiv 

func (v I2) MulDiv(n, d int64) I2

MulDiv does both scalar multiplication and division, and tries to avoid overflow on 32-bit.

func (I2) Normal 

func (v I2) Normal() I2

Normal returns a vector perpendicular to v of the same length.

func (I2) Sgn 

func (v I2) Sgn() I2

Sgn returns a "unit-ish" vector (each component is normalised).

func (I2) Sub 

func (v I2) Sub(w I2) I2

Sub returns v - w.

func (I2) Swap 

func (v I2) Swap() I2

Swap switches x and y components.

type Rect 

type Rect struct {
	UL, DR I2
}

func NewRect 

func NewRect(x0, y0, x1, y1 int) Rect

func (Rect) C 

func (r Rect) C() (x0, y0, x1, y1 int)

func (Rect) Contains 

func (r Rect) Contains(p I2) bool

func (Rect) Expand 

func (r Rect) Expand(e I2) Rect

func (Rect) Overlaps 

func (r Rect) Overlaps(s Rect) bool

func (Rect) Reposition 

func (r Rect) Reposition(ul I2) Rect

func (Rect) Resize 

func (r Rect) Resize(sz I2) Rect

func (Rect) Size 

func (r Rect) Size() I2

func (Rect) Translate 

func (r Rect) Translate(p I2) Rect

type VertexSet 

type VertexSet map[I2]bool

VertexSet is a set of vertices.

Source Files

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