ICurve

Description

interface Tinman.Terrain.Util.ICurve

Derived from: IEquatable<ICurve>
ISerializable
IConfigurable
IVersioned
Extended by: Curve ^abstract

Base interface for classes that represent a curve that interpolates through a sequence of control points.

A curve has zero or more control points, which may be added with the Add* methods and cleared with Clear. Each control point has a required position value and an optional tangent value. Each value is a tuple with 1 to 4 components. By replicating control points, the curve can be further adjusted (see Replicate). Control point information may be queried with Count, Range, HasTangents and GetAt. Interpolation of points (1D through 4D) along the curve is performed by the Compute* methods. With Length, WalkIndex and WalkDistance, spatial information about the curve is exposed. Regarding WalkDistance and WalkIndex, the following holds true:

A,B := control point indices within valid range

WalkIndex(A, WalkDistance(A, B)) ~= B
WalkIndex(B, WalkDistance(B, A)) ~= A

(only almost equal because of numeric algorithm)

WalkDistance(A, B) = -WalkDistance(B, A)

Walking along a curve is implemented with a recursive numeric algorithm and may involve significant floating-point calculations. Computing the walk distance between integral control point indices will use an internal cache of walk distance values and thus reduces to a simple lookup-table query.

See also: Curve.Tangent
Curve.New

Public / Methods

Add

_4 overloads

public method Add¹ → (1)

px ⁱⁿ : float64: X-coordinate (position) of the control point.
returns → ICurve: this

Adds a control point to this curve.

Using this method on a curve that has tangents will specify zero for tangent values.

See also: ICurve.HasTangents
ICurve.Replicate

public method Add² → (2)

px ⁱⁿ : float64: X-coordinate (position) of the control point.
py ⁱⁿ : float64: Y-coordinate (position) of the control point.
returns → ICurve: this

Adds a control point to this curve.

Using this method on a curve that has tangents will specify zero for tangent values.

See also: ICurve.HasTangents
ICurve.Replicate

public method Add³ → (3)

px ⁱⁿ : float64: X-coordinate (position) of the control point.
py ⁱⁿ : float64: Y-coordinate (position) of the control point.
pz ⁱⁿ : float64: Z-coordinate (position) of the control point.
returns → ICurve: this

Adds a control point to this curve.

Using this method on a curve that has tangents will specify zero for tangent values.

See also: ICurve.HasTangents
ICurve.Replicate

public method Add⁴ → (4)

px ⁱⁿ : float64: X-coordinate (position) of the control point.
py ⁱⁿ : float64: Y-coordinate (position) of the control point.
pz ⁱⁿ : float64: Z-coordinate (position) of the control point.
pw ⁱⁿ : float64: W-coordinate (position) of the control point.
returns → ICurve: this

Adds a control point to this curve.

Using this method on a curve that has tangents will specify zero for tangent values.

See also: ICurve.HasTangents
ICurve.Replicate

Add2

_4 overloads

public method Add2¹ → (2)

px ⁱⁿ : float64: X-coordinate (position) of the control point.
tx ⁱⁿ : float64: X-coordinate (tangent) of the control point.
returns → ICurve: this

Adds a control point to this curve.

Using this method on a curve that does not have tangents will discard the tangent values.

See also: ICurve.HasTangents
ICurve.Replicate

public method Add2² → (4)

px ⁱⁿ : float64: X-coordinate (position) of the control point.
tx ⁱⁿ : float64: X-coordinate (tangent) of the control point.
py ⁱⁿ : float64: Y-coordinate (position) of the control point.
ty ⁱⁿ : float64: Y-coordinate (tangent) of the control point.
returns → ICurve: this

Adds a control point to this curve.

Using this method on a curve that does not have tangents will discard the tangent values.

See also: ICurve.HasTangents
ICurve.Replicate

public method Add2³ → (6)

px ⁱⁿ : float64: X-coordinate (position) of the control point.
tx ⁱⁿ : float64: X-coordinate (tangent) of the control point.
py ⁱⁿ : float64: Y-coordinate (position) of the control point.
ty ⁱⁿ : float64: Y-coordinate (tangent) of the control point.
pz ⁱⁿ : float64: Z-coordinate (position) of the control point.
tz ⁱⁿ : float64: Z-coordinate (tangent) of the control point.
returns → ICurve: this

Adds a control point to this curve.

Using this method on a curve that does not have tangents will discard the tangent values.

See also: ICurve.HasTangents
ICurve.Replicate

public method Add2⁴ → (8)

px ⁱⁿ : float64: X-coordinate (position) of the control point.
tx ⁱⁿ : float64: X-coordinate (tangent) of the control point.
py ⁱⁿ : float64: Y-coordinate (position) of the control point.
ty ⁱⁿ : float64: Y-coordinate (tangent) of the control point.
pz ⁱⁿ : float64: Z-coordinate (position) of the control point.
tz ⁱⁿ : float64: Z-coordinate (tangent) of the control point.
pw ⁱⁿ : float64: W-coordinate (position) of the control point.
tw ⁱⁿ : float64: W-coordinate (tangent) of the control point.
returns → ICurve: this

Adds a control point to this curve.

Using this method on a curve that does not have tangents will discard the tangent values.

See also: ICurve.HasTangents
ICurve.Replicate

Clear

public method Clear → ()

returns → ICurve: this

Removes all control points from this curve.

Compute1D

[Pure]
public method Compute1D → (1)

index ⁱⁿ : float64: The control point index.
returns → float64: The computed point or Maths.NanD if the curve has no control points.

Computes a 1D point along this curve.

Compute2D

[Pure]
public method Compute2D → (1)

index ⁱⁿ : float64: The control point index.
returns → Vec2D: The computed point or Vec2D.Undefined if the curve has no control points.

Computes a 2D point along this curve.

Compute3D

[Pure]
public method Compute3D → (1)

index ⁱⁿ : float64: The control point index.
returns → Vec3D: The computed point or Vec3D.Undefined if the curve has no control points.

Computes a 3D point along this curve.

Compute4D

[Pure]
public method Compute4D → (1)

index ⁱⁿ : float64: The control point index.
returns → Vec4D: The computed point or Vec4D.Undefined if the curve has no control points.

Computes a 4D point along this curve.

GetAt

[Pure]
public method GetAt → (2)

index ⁱⁿ : int32: [0..ICurve.Count-1]
The control point index.
which ^opt : int32 = 0: Chooses the control point value:
< 0 : the incoming tangent value,
= 0 : the position value,
> 0 : the outgoing tangent value.
returns → Vec4D: The control point.

Returns a control point.

WalkDistance

[Pure]
public method WalkDistance → (2)

start ⁱⁿ : float64: The start control point index. Will be clamped to Range.
end ⁱⁿ : float64: The end control point index. Will be clamped to Range.
returns → float64: The walk distance from start ⁱⁿ to end ⁱⁿ along the curve, using Compute3D for distance computations.

Computes the walk distance from the given start control point to the given end control point.

See also: ICurve.WalkIndex

WalkIndex

[Pure]
public method WalkIndex → (2)

index ⁱⁿ : float64: The index of the control point where to start walking.
distance ⁱⁿ : float64: The distance to walk from the given control point. Positive distance values increase the control point index, negative distance values decrease it.
returns → float64: The resulting control point index.

Walks along this curve for the given distance ⁱⁿ, starting at the given control point.

See also: ICurve.WalkDistance

Public / Attributes

Continuity

[Constant]
public attribute Continuity → (get)

value : Continuity: The continuity of this curve.

The continuity type of this curve.

Count

public attribute Count → (get)

value : int32: [>=0]
The number of control points.

The number of control points.

See also: ICurve.Range

HasTangents

[Constant]
public attribute HasTangents → (get)

value : bool: true if control points have tangent values,
false if control points do not have tangent values.

Does this curve have tangent values for control points?

Length

public attribute Length → (get)

value : float64: [>=0]
The curve length, given as the walk distance from the first control point to the last.

Returns the length curve.

Getting this value is equivalent to calling WalkDistance for Range.

Range

public attribute Range → (get)

value : RangeD: The control point index range, where RangeD.Start is always zero. Will be RangeD.Zero if Count is 1 or less.

Returns the range of control point indices.

Control points within this range can be used to compute points, without clamping at the first and last control points.

Replicate

[Constant]
public attribute Replicate → (get)

value : int32: [0..2]
The replication count, see remarks.

Returns how many times a control point may be replicated, in order to control the curve.

A control point is replicated by calling one of the Add* methods, passing identical position values. The replication count values have the following meaning:

Replicate = 2
When Continuity is Continuity.Curvature, replicating a control point once or twice reduces to Continuity.Tangent or Continuity.Position, respectively. The first and the last control point may only be replicated at most once, to avoid curve segments of zero length.
Replicate = 1
When Continuity is Continuity.Tangent and HasTangents is true, the original control point defines the incoming tangent values and the last replicated control point defines the outgoing tangent values. If the incoming and outgoing tangent values are different, Continuity reduces to Continuity.Position.
Replicate = 0
Replicated control points will be discarded.

Since the Add* methods will drop control points when the replication count is exceeded, the caller must not assume Count, Length or Range is incremented for each call.

Extensions

Add

_3 overloads

public static method Add¹ → (1)

p ⁱⁿ : Vec2D: The control point (position).
returns → ICurve: this

Adds a control point to this curve.

Using this method on a curve that has tangents will specify zero for tangent values.

See also: ICurve.HasTangents
ICurve.Replicate

public static method Add² → (1)

p ⁱⁿ : Vec3D: The control point (position).
returns → ICurve: this

Adds a control point to this curve.

Using this method on a curve that has tangents will specify zero for tangent values.

See also: ICurve.HasTangents
ICurve.Replicate

public static method Add³ → (1)

p ⁱⁿ : Vec4D: The control point (position).
returns → ICurve: this

Adds a control point to this curve.

Using this method on a curve that has tangents will specify zero for tangent values.

See also: ICurve.HasTangents
ICurve.Replicate

Add2

_3 overloads

public static method Add2¹ → (2)

p ⁱⁿ : Vec2D: The control point (position).
t ⁱⁿ : Vec2D: The control point (tangent).
returns → ICurve: this

Adds a control point to this curve.

Using this method on a curve that does not have tangents will discard the tangent values.

See also: ICurve.HasTangents
ICurve.Replicate

public static method Add2² → (2)

p ⁱⁿ : Vec3D: The control point (position).
t ⁱⁿ : Vec3D: The control point (tangent).
returns → ICurve: this

Adds a control point to this curve.

Using this method on a curve that does not have tangents will discard the tangent values.

See also: ICurve.HasTangents
ICurve.Replicate

public static method Add2³ → (2)

p ⁱⁿ : Vec4D: The control point (position).
t ⁱⁿ : Vec4D: The control point (tangent).
returns → ICurve: this

Adds a control point to this curve.

Using this method on a curve that does not have tangents will discard the tangent values.

See also: ICurve.HasTangents
ICurve.Replicate

WalkDistance

[Pure]
public static method WalkDistance → (1)

range ⁱⁿ : RangeD: The control point index range. Will be clamped to Range.
returns → float64: The walk distance from RangeD.Start to RangeD.End.

Computes the walk distance from the given start control point to the given end control point.

See also: ICurve.WalkIndex

ICurve

Description

Public / Methods

Add

Add2

Clear

Compute1​D

Compute2​D

Compute3​D

Compute4​D

Get​At

Walk​Distance

Walk​Index

Public / Attributes

Continuity

Count

Has​Tangents

Length

Range

Replicate

Extensions

Add

Add2

Walk​Distance

Compute1D

Compute2D

Compute3D

Compute4D

GetAt

WalkDistance

WalkIndex

HasTangents

WalkDistance