Struct FractionalHexCoord

Represents a fractional (floating-point) coordinate in hexagonal cube space. Used as an intermediate value during world-to-grid conversion and line drawing, then rounded to the nearest HexCoord using the cube rounding algorithm.

Implements

IEquatable<FractionalHexCoord>

Inherited Members

object.Equals(object, object)

object.GetType()

object.ReferenceEquals(object, object)

Namespace: Scylla.Core.Structures

Assembly: ScyllaCore.dll

Syntax

public readonly struct FractionalHexCoord : IEquatable<FractionalHexCoord>

Remarks

FractionalHexCoord follows the same axial convention as HexCoord: only Q and R are stored; S is computed on demand as -Q - R.

The primary use cases are:

• World-to-grid snapping: WorldToGrid(Vector2) internally creates a FractionalHexCoord and calls Round().
• Hex line drawing: Lerp(FractionalHexCoord, FractionalHexCoord, float) interpolates between two integer endpoints to produce a sequence of fractional samples that are individually rounded.

Equality comparison uses exact floating-point equality (bit-identical Q and R values). For approximate comparison, round both values first and compare the resulting HexCoord instances.

Constructors

FractionalHexCoord(float, float)

Creates a new fractional hex coordinate with the specified axial values.

Declaration

public FractionalHexCoord(float q, float r)

Parameters

Type	Name	Description
float	q	The fractional Q axis value (column). May be any finite float.
float	r	The fractional R axis value (row). May be any finite float.

Fields

Q

The fractional Q axis value (column in axial coordinates).

Declaration

public readonly float Q

Field Value

Type	Description
float

R

The fractional R axis value (row in axial coordinates).

Declaration

public readonly float R

Field Value

Type	Description
float

Properties

S

The computed fractional S axis value: -Q - R. Not stored directly; computed on demand to maintain the cube constraint Q + R + S = 0.

Declaration

public float S { get; }

Property Value

Type	Description
float

Methods

Equals(FractionalHexCoord)

Determines whether this coordinate equals another coordinate using exact float comparison. For approximate comparison, use Round() and compare the resulting HexCoord values.

Declaration

public bool Equals(FractionalHexCoord other)

Parameters

Type	Name	Description
FractionalHexCoord	other	The coordinate to compare with.

Returns

Type	Description
bool	True if both coordinates have identical Q and R values.

Equals(object)

Determines whether this coordinate equals another object.

Declaration

public override bool Equals(object obj)

Parameters

Type	Name	Description
object	obj	The object to compare with.

Returns

Type	Description
bool	True if the object is a FractionalHexCoord with equal values.

Overrides

ValueType.Equals(object)

GetHashCode()

Returns a hash code for this fractional coordinate.

Declaration

public override int GetHashCode()

Returns

Type	Description
int	A hash code based on Q and R.

Overrides

ValueType.GetHashCode()

Lerp(FractionalHexCoord, FractionalHexCoord, float)

Linearly interpolates between two fractional hex coordinates. Interpolation is applied independently to the Q and R axes. The result can be rounded to the nearest integer hex using Round(), which is the basis for hex line drawing.

Declaration

public static FractionalHexCoord Lerp(FractionalHexCoord a, FractionalHexCoord b, float t)

Parameters

Type	Name	Description
FractionalHexCoord	a	The start coordinate (t = 0).
FractionalHexCoord	b	The end coordinate (t = 1).
float	t	The interpolation factor. Values outside [0, 1] extrapolate beyond the segment endpoints.

Returns

Type	Description
FractionalHexCoord	The interpolated fractional coordinate between a and b.

Round()

Rounds this fractional coordinate to the nearest integer hex coordinate using the cube rounding algorithm (Charles Fu, 1994).

Declaration

public HexCoord Round()

Returns

Type	Description
HexCoord	The HexCoord whose center is closest to this fractional position in cube space.

Remarks

The algorithm rounds all three cube components (Q, R, S) independently, then detects which component has the largest rounding error. That component is recomputed from the other two (roundQ = -roundR - roundS, etc.) to satisfy the constraint Q + R + S = 0. This is the standard robust hex-rounding technique and avoids bias artifacts that simpler rounding strategies produce near hex boundaries.

ToString()

Returns a string representation of this fractional coordinate.

Declaration

public override string ToString()

Returns

Type	Description
string	A string in the format "(Q, R)".

Overrides

ValueType.ToString()

Operators

operator ==(FractionalHexCoord, FractionalHexCoord)

Returns true if left and right have bit-identical Q and R values.

Declaration

public static bool operator ==(FractionalHexCoord left, FractionalHexCoord right)

Parameters

Type	Name	Description
FractionalHexCoord	left	The left operand.
FractionalHexCoord	right	The right operand.

Returns

Type	Description
bool

operator !=(FractionalHexCoord, FractionalHexCoord)

Returns true if left and right differ in Q or R.

Declaration

public static bool operator !=(FractionalHexCoord left, FractionalHexCoord right)

Parameters

Type	Name	Description
FractionalHexCoord	left	The left operand.
FractionalHexCoord	right	The right operand.

Returns

Type	Description
bool

Implements

IEquatable<T>