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Published: Apr 21, 2023 License: Apache-2.0 Imports: 3 Imported by: 93



Package r2 implements types and functions for working with geometry in ℝ².

See package s2 for a more detailed overview.



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type Point

type Point struct {
	X, Y float64

Point represents a point in ℝ².

func (Point) Add

func (p Point) Add(op Point) Point

Add returns the sum of p and op.

func (Point) Cross

func (p Point) Cross(op Point) float64

Cross returns the cross product of p and op.

func (Point) Dot

func (p Point) Dot(op Point) float64

Dot returns the dot product between p and op.

func (Point) Mul

func (p Point) Mul(m float64) Point

Mul returns the scalar product of p and m.

func (Point) Norm

func (p Point) Norm() float64

Norm returns the vector's norm.

func (Point) Normalize

func (p Point) Normalize() Point

Normalize returns a unit point in the same direction as p.

func (Point) Ortho

func (p Point) Ortho() Point

Ortho returns a counterclockwise orthogonal point with the same norm.

func (Point) String

func (p Point) String() string

func (Point) Sub

func (p Point) Sub(op Point) Point

Sub returns the difference of p and op.

type Rect

type Rect struct {
	X, Y r1.Interval

Rect represents a closed axis-aligned rectangle in the (x,y) plane.

func EmptyRect

func EmptyRect() Rect

EmptyRect constructs the canonical empty rectangle. Use IsEmpty() to test for empty rectangles, since they have more than one representation. A Rect{} is not the same as the EmptyRect.

func RectFromCenterSize

func RectFromCenterSize(center, size Point) Rect

RectFromCenterSize constructs a rectangle with the given center and size. Both dimensions of size must be non-negative.

func RectFromPoints

func RectFromPoints(pts ...Point) Rect

RectFromPoints constructs a rect that contains the given points.

func (Rect) AddPoint

func (r Rect) AddPoint(p Point) Rect

AddPoint expands the rectangle to include the given point. The rectangle is expanded by the minimum amount possible.

func (Rect) AddRect

func (r Rect) AddRect(other Rect) Rect

AddRect expands the rectangle to include the given rectangle. This is the same as replacing the rectangle by the union of the two rectangles, but is more efficient.

func (Rect) ApproxEqual

func (r Rect) ApproxEqual(r2 Rect) bool

ApproxEqual returns true if the x- and y-intervals of the two rectangles are the same up to the given tolerance.

func (Rect) Center

func (r Rect) Center() Point

Center returns the center of the rectangle in (x,y)-space

func (Rect) ClampPoint

func (r Rect) ClampPoint(p Point) Point

ClampPoint returns the closest point in the rectangle to the given point. The rectangle must be non-empty.

func (Rect) Contains

func (r Rect) Contains(other Rect) bool

Contains reports whether the rectangle contains the given rectangle.

func (Rect) ContainsPoint

func (r Rect) ContainsPoint(p Point) bool

ContainsPoint reports whether the rectangle contains the given point. Rectangles are closed regions, i.e. they contain their boundary.

func (Rect) Expanded

func (r Rect) Expanded(margin Point) Rect

Expanded returns a rectangle that has been expanded in the x-direction by margin.X, and in y-direction by margin.Y. If either margin is empty, then shrink the interval on the corresponding sides instead. The resulting rectangle may be empty. Any expansion of an empty rectangle remains empty.

func (Rect) ExpandedByMargin

func (r Rect) ExpandedByMargin(margin float64) Rect

ExpandedByMargin returns a Rect that has been expanded by the amount on all sides.

func (Rect) Hi

func (r Rect) Hi() Point

Hi returns the high corner of the rect.

func (Rect) InteriorContains

func (r Rect) InteriorContains(other Rect) bool

InteriorContains reports whether the interior of this rectangle contains all of the points of the given other rectangle (including its boundary).

func (Rect) InteriorContainsPoint

func (r Rect) InteriorContainsPoint(p Point) bool

InteriorContainsPoint returns true iff the given point is contained in the interior of the region (i.e. the region excluding its boundary).

func (Rect) InteriorIntersects

func (r Rect) InteriorIntersects(other Rect) bool

InteriorIntersects reports whether the interior of this rectangle intersects any point (including the boundary) of the given other rectangle.

func (Rect) Intersection

func (r Rect) Intersection(other Rect) Rect

Intersection returns the smallest rectangle containing the intersection of this rectangle and the given rectangle.

func (Rect) Intersects

func (r Rect) Intersects(other Rect) bool

Intersects reports whether this rectangle and the other rectangle have any points in common.

func (Rect) IsEmpty

func (r Rect) IsEmpty() bool

IsEmpty reports whether the rectangle is empty.

func (Rect) IsValid

func (r Rect) IsValid() bool

IsValid reports whether the rectangle is valid. This requires the width to be empty iff the height is empty.

func (Rect) Lo

func (r Rect) Lo() Point

Lo returns the low corner of the rect.

func (Rect) Size

func (r Rect) Size() Point

Size returns the width and height of this rectangle in (x,y)-space. Empty rectangles have a negative width and height.

func (Rect) String

func (r Rect) String() string

func (Rect) Union

func (r Rect) Union(other Rect) Rect

Union returns the smallest rectangle containing the union of this rectangle and the given rectangle.

func (Rect) VertexIJ

func (r Rect) VertexIJ(i, j int) Point

VertexIJ returns the vertex in direction i along the X-axis (0=left, 1=right) and direction j along the Y-axis (0=down, 1=up).

func (Rect) Vertices

func (r Rect) Vertices() [4]Point

Vertices returns all four vertices of the rectangle. Vertices are returned in CCW direction starting with the lower left corner.

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