/// <summary>
/// Gives a new point that represents the
/// first point multiplied by the second point
/// component-wise.
///
/// Since version 1.6 (Rect)
/// Since version 1.7 (other)
/// </summary>
public PointyHexPoint Mul(PointyHexPoint otherPoint)
{
var x = X * otherPoint.X;
var y = Y * otherPoint.Y;
return(new PointyHexPoint(x, y));
}
public IEnumerable <PointyHexPoint> GetSpiralIterator(PointyHexPoint origin, int ringCount)
{
var hexPoint = origin;
yield return(hexPoint);
for (var k = 1; k < ringCount; k++)
{
hexPoint = new PointyHexPoint(0, 0);
hexPoint = hexPoint + SpiralIteratorDirections[4] * (k);
for (var i = 0; i < 6; i++)
{
for (var j = 0; j < k; j++)
{
if (Contains(hexPoint))
{
yield return(hexPoint);
}
hexPoint = hexPoint + SpiralIteratorDirections[i];
}
}
}
}
public PointyHexShapeInfo <TCell> Hexagon(int side)
{
var storageSize = 2 * side - 1;
var storageBottomLeft = new PointyHexPoint(1 - side, 1 - side);
return(Shape(storageSize, storageSize, x => IsInsideHex(x, side), storageBottomLeft));
}
/**
* @since 1.7
*/
public IEnumerable <PointyHexPoint> GetSpiralIterator(int N)
{
var hexPoint = new PointyHexPoint(0, 0);
yield return(hexPoint);
for (var k = 0; k < N; k++)
{
hexPoint = new PointyHexPoint(0, 0);
hexPoint = hexPoint + HexDirections[4] * (k);
for (var i = 0; i < 6; i++)
{
for (var j = 0; j < k; j++)
{
if (Contains(hexPoint))
{
yield return(hexPoint);
}
hexPoint = hexPoint + HexDirections[i];
}
}
}
}
/// <summary>
/// Gives a new point that represents the
/// first point divided by the second point
/// component-wise. The division is integer
/// division.
///
/// Since version 1.6 (Rect)
/// Since version 1.7 (other)
/// </summary>
public PointyHexPoint Div(PointyHexPoint otherPoint)
{
var x = GLMathf.FloorDiv(X, otherPoint.X);
var y = GLMathf.FloorDiv(Y, otherPoint.Y);
return(new PointyHexPoint(x, y));
}
/**
* Makes an edge grid for this grid.
*/
public IGrid <TNewCell, PointyRhombPoint> MakeEdgeGrid <TNewCell>()
{
var edgeOffset = GridOrigin;
var offset = new PointyHexPoint(1, 1);
return(new PointyRhombGrid <TNewCell>(width + 2, height + 2, x => IsInsideEdgeGrid(x - offset), edgeOffset.GetEdgeAnchor().BasePoint - offset));
}
public PointyHexShapeInfo <TCell> FatRectangle(int width, int height)
{
int storageWidth = width + GLMathf.FloorDiv(height, 2);
int storageHeight = height;
var storageBottomLeft = new PointyHexPoint(-GLMathf.FloorDiv(height, 2), 0);
return(Shape(storageWidth, storageHeight, x => IsInsideFatRectangle(x, width, height), storageBottomLeft));
}
private static bool IsInsideXYParallelogram(PointyHexPoint point, int width, int height)
{
return
((point.X >= 0) &&
(point.X < width) &&
(point.Y >= 0) &&
(point.Y < height));
}
public static bool DefaultContains(PointyHexPoint point, int width, int height)
{
ArrayPoint storagePoint = ArrayPointFromGridPoint(point);
return
(storagePoint.X >= 0 &&
storagePoint.X < width &&
storagePoint.Y >= 0 &&
storagePoint.Y < height);
}
private static bool IsInsideFatRectangle(PointyHexPoint point, int width, int height)
{
int startX = -(GLMathf.FloorDiv(point.Y, 2));
return
(point.X >= startX - GLMathf.FloorMod(point.Y, 2) &&
point.X < startX + width &&
point.Y >= 0 &&
point.Y < height);
}
/**
* Rotates a shape 180 degrees around the edge shared by the two given points.
*
* The two points must be neighbors.
*/
public static IEnumerable <PointyHexPoint> Rotate180About(
IEnumerable <PointyHexPoint> shape,
PointyHexPoint p1,
PointyHexPoint p2)
{
var translation = p1.Translate(p2);
var correction = translation.Subtract(translation.Rotate180()).ScaleDown(2);
return(TransformShape <PointyHexPoint>(shape, point => point.Rotate180().Translate(correction)).ToList());
}
/**
* Rotates a shape 120 degrees around the vertice shared by the three given points.
*
* The three points must form a close triangle (they must share a vertex).
*/
public static IEnumerable <PointyHexPoint> Rotate120About(
IEnumerable <PointyHexPoint> shape,
PointyHexPoint p1,
PointyHexPoint p2,
PointyHexPoint p3)
{
/*
* If t = (p1 + p2 + p3)/3, then the result is p => (p - t).Rotate120() + t.
*
* This can be rewritten p => p.Rotate120() - t.Rotate120() + t
* = p.Rotate120() (T - T.Rotate120())/3,
* where T = p1 + p2 + p3.
*
* This is what this method calculates. This is done so that all coordinates in
* intermediatary calculations stay integers.
*/
var translation = p1.Translate(p2.Translate(p3));
var correction = translation.Subtract(translation.Rotate120()).ScaleDown(3);
return(TransformShape(shape, point => point.Rotate120().Translate(correction)).ToList());
}
/// <summary>
/// Gives a coloring of the grid such that
/// if a point p has color k, then all points
/// p + m[ux, 0] + n[vx, vy] have the same color
/// for any integers a and b.
///
/// More information anout grid colorings:
/// http://gamelogic.co.za/2013/12/18/what-are-grid-colorings/
///
/// Since version 1.7
/// </summary>
public int __GetColor__ReferenceImplementation(int ux, int vx, int vy)
{
var u = new PointyHexPoint(ux, 0);
var v = new PointyHexPoint(vx, vy);
int colorCount = u.PerpDot(v);
float a = PerpDot(v) / (float)colorCount;
float b = -PerpDot(u) / (float)colorCount;
int m = Mathf.FloorToInt(a);
int n = Mathf.FloorToInt(b);
int baseVectorX = m * u.X + n * v.X;
int baseVectorY = n * u.Y + n * v.Y;
int offsetX = GLMathf.FloorMod(X - baseVectorX, ux);
int offsetY = Y - baseVectorY;
int colorIndex = Mathf.FloorToInt(offsetX + offsetY * ux);
return(colorIndex);
}
/**
* Whether this point is in the hexagon with the given radius
* and given center.
*
* A single point is considered a hexagon with zero radius.
*
* @sa http://devmag.org.za/2013/08/31/geometry-with-hex-coordinates/
*
* @since 1.3
*/
public bool IsInsideHexagon(PointyHexPoint center, int radius)
{
return((this - center).Magnitude() <= radius);
}
protected override CairoGrid <TCell> MakeShape(int x, int y, Func <CairoPoint, bool> isInside, PointyHexPoint offset)
{
return(new CairoGrid <TCell>(x, y, isInside, offset));
}
protected override ArrayPoint ArrayPointFromGridPoint(PointyHexPoint point)
{
return(CairoGrid <TCell> .ArrayPointFromGridPoint(point));
}
protected override PointyRhombGrid <TCell> MakeShape(int x, int y, Func <PointyRhombPoint, bool> isInside, PointyHexPoint offset)
{
return(new PointyRhombGrid <TCell>(x, y, isInside, offset));
}
protected override FlatTriGrid <TCell> MakeShape(int x, int y, Func <FlatTriPoint, bool> isInside, PointyHexPoint offset)
{
return(new FlatTriGrid <TCell>(x, y, isInside, offset));
}
protected override CairoPoint MakePoint(PointyHexPoint basePoint, int index)
{
return(new CairoPoint(basePoint.X, basePoint.Y, index));
}
/**
* Construct a new grid whose cells are determined by the given test function.
*
* The function should only return true for points within the bounds of the rectangle when
* the given transforms are applied to them.
*
* Normally, the static factory methods or shape building methods should be used to create grids.
* These constructors are provided for advanced usage.
*
* @link_constructing_grids
*/
public PointyHexGrid(int width, int height, Func <PointyHexPoint, bool> isInside, PointyHexPoint offset) :
this(width, height, isInside, x => x.MoveBy(offset), x => x.MoveBackBy(offset), PointyHexPoint.MainDirections)
{
}
public static ArrayPoint ArrayPointFromGridPoint(PointyHexPoint point)
{
return(PointyHexGrid <TCell> .ArrayPointFromGridPoint(point));
}
public InspectableVectorPoint(PointyHexPoint point)
{
x = point.X;
y = point.Y;
}
protected override PointyRhombPoint MakePoint(PointyHexPoint basePoint, int index)
{
return(new PointyRhombPoint(basePoint.X, basePoint.Y, index));
}
public static ArrayPoint ArrayPointFromGridPoint(PointyHexPoint point)
{
return(new ArrayPoint(point.X, point.Y));
}
override protected ArrayPoint ArrayPointFromPoint(PointyHexPoint hexPoint)
{
return(ArrayPointFromGridPoint(hexPoint));
}
/**
* Use this function to create shapes to ensure they fit into memory.
*
* The test function can test shapes anywhere in space. If you specify the bottom corner
* (in terms of the storage rectangle), the shape is automatically translated in memory
* to fit, assuming memory width and height is big enough.
*
* Strategy for implementing new shapes:
* - First, determine the test function.
* - Next, draw a storage rectangle that contains the shape.
* - Determine the storgae rectangle width and height.
* - Finally, determine the grid-space coordinate of the left bottom corner of the storage rectangle.
*
* Then define your function as follows:
*
* \code{cs}
* public PointyRhombShapeInfo<TCell> MyShape()
* {
* Shape(stargeRectangleWidth, storageRectangleHeight, isInsideMyShape, storageRectangleBottomleft);
* }
* \endcode
*
* \param width The widh of the storage rectangle
* \param height The height of the storage rectangle
* \param isInside A function that returns true if a passed point lies inside the shape being defined
* \param bottomLeftCorner The grid-space coordinate of the bottom left corner of the storage rect.
*
*/
public PointyRhombShapeInfo <TCell> Shape(int width, int height, Func <PointyRhombPoint, bool> isInside, PointyHexPoint bottomLeftCorner)
{
var shapeInfo = MakeShapeStorageInfo <PointyRhombPoint>(width, height, x => isInside(x + bottomLeftCorner));
return(new PointyRhombShapeInfo <TCell>(shapeInfo).Translate(bottomLeftCorner));
}
protected override FlatTriPoint MakePoint(PointyHexPoint basePoint, int index)
{
return(new FlatTriPoint(basePoint.X, basePoint.Y, index));
}
public int Dot(PointyHexPoint other)
{
return(x * other.X + y * other.Y);
}
public CairoGrid(int width, int height, Func <CairoPoint, bool> isInside, PointyHexPoint offset) :
this(width, height, isInside, x => x.Translate(offset), x => x.Translate(offset.Negate()))
{
}
public int PerpDot(PointyHexPoint other)
{
return(x * other.Y - y * other.x);
}