Geom2D.CubicBezier.Approximate

Documentation

approximatePath

Arguments

:: (Unbox a, Ord a, Floating a)

=> (a -> (Point a, Point a))

The function to approximate and it's derivative

-> Int

The number of discrete samples taken to approximate each subcurve. More samples are more precise but take more time to calculate. For good precision 16 is a good candidate.

-> a

The tolerance

-> a

The lower parameter of the function

-> a

The upper parameter of the function

-> Bool

Calculate the result faster, but with more subcurves. Runs typically 10 times faster, but generates 50% more subcurves. Useful for interactive use.

-> [CubicBezier a]

Approximate a function with piecewise cubic bezier splines using a least-squares fit, within the given tolerance. Each subcurve is approximated by using a finite number of samples. It is recommended to avoid changes in direction by subdividing the original function at points of inflection.

approximateQuadPath

Arguments

:: (Show a, Unbox a, Ord a, Floating a)

=> (a -> (Point a, Point a))

The function to approximate and it's derivative

-> a

The tolerance

-> a

The lower parameter of the function

-> a

The upper parameter of the function

-> Bool

Calculate the result faster, but with more subcurves.

-> [QuadBezier a]

Approximate a function with piecewise quadratic bezier splines using a least-squares fit, within the given tolerance. It is recommended to avoid changes in direction by subdividing the original function at points of inflection.

approximatePathMax

Arguments

:: (Unbox a, Floating a, Ord a)

=> Int

The maximum number of subcurves

-> (a -> (Point a, Point a))

The function to approximate and it's derivative

-> Int

The number of discrete samples taken to approximate each subcurve. More samples are more precise but take more time to calculate. For good precision 16 is a good candidate.

-> a

The tolerance

-> a

The lower parameter of the function

-> a

The upper parameter of the function

-> Bool

Calculate the result faster, but with more subcurves. Runs faster (typically 10 times), but generates more subcurves (about 50%). Useful for interactive use.

-> [CubicBezier a]

Like approximatePath, but limit the number of subcurves.

approximateQuadPathMax

Arguments

:: (Unbox a, Show a, Floating a, Ord a)

=> Int

The maximum number of subcurves

-> (a -> (Point a, Point a))

The function to approximate and it's derivative

-> a

The tolerance

-> a

The lower parameter of the function

-> a

The upper parameter of the function

-> Bool

Calculate the result faster, but with more subcurves. Runs faster, but generates more subcurves. Useful for interactive use.

-> [QuadBezier a]

Like approximateQuadPath, but limit the number of subcurves.

approximateCubic

Arguments

:: (Unbox a, Ord a, Floating a)

=> CubicBezier a

Curve

-> Vector (Point a)

Points

-> Maybe (Vector a)

Params. Approximate if Nothing

-> Int

Maximum iterations

-> (CubicBezier a, a)

result curve and maximum error

approximateCubic b pts maxiter finds the least squares fit of a bezier curve to the points pts. The resulting bezier has the same first and last control point as the curve b, and have tangents colinear with b.