Geom2D.CubicBezier.Numeric

Numerical computations used by the cubic bezier functions. Also contains functions that aren't used anymore, but might be useful on its own.

Documentation

quadraticRoot :: Double -> Double -> Double -> [Double]

quadraticRoot a b c find the real roots of the quadratic equation a x^2 + b x + c = 0. It will return one, two or zero roots.

cubicRoot :: Double -> Double -> Double -> Double -> [Double]

cubicRootNorm :: Double -> Double -> Double -> [Double]

Find real roots from the normalized cubic equation.

solveLinear2x2 :: (Eq a, Fractional a) => a -> a -> a -> a -> a -> a -> Maybe (a, a)

solveLinear2x2 a b c d e f solves the linear equation with two variables (x and y) and two systems:

a x + b y + c = 0
d x + e y + f = 0

Returns Nothing if no solution is found.

goldSearch :: (Ord a, Floating a) => (a -> a) -> Int -> a

makeSparse

Arguments

:: Unbox a

=> Vector Int

The column index of the first element of each row. Should be ascending in order.

-> Matrix a

The adjacent coefficients in each row

-> SparseMatrix a

A sparse matrix.

data SparseMatrix a

sparseMulT :: (Num a, Unbox a) => Vector a -> SparseMatrix a -> Vector a

Multiply the vector by the transpose of the sparse matrix.

sparseMul :: (Num a, Unbox a) => SparseMatrix a -> Vector a -> Vector a

Sparse matrix * vector multiplication.

addMatrix :: (Num a, Unbox a) => Matrix a -> Matrix a -> Matrix a

addVec :: (Num a, Unbox a) => Vector a -> Vector a -> Vector a

lsqMatrix

Arguments

:: (Num a, Unbox a)

=> SparseMatrix a

The input system.

-> Matrix a

The resulting symmetric matrix as a sparse matrix. The first element of each row is the element on the diagonal.

Given a rectangular matrix M, calculate the symmetric square matrix MᵀM which can be used to find a least squares solution to the overconstrained system.

lsqSolveDist

Arguments

:: (Fractional a, Unbox a)

=> SparseMatrix (a, a)

sparse matrix

-> Vector (a, a)

Right hand side vector.

-> Vector a

Solution vector

lsqSolveDist rowStart M y Find a least squares solution of the distance between the points.

decompLDL :: (Fractional a, Unbox a) => Matrix a -> Matrix a

LDL* decomposition of the sparse hermitian matrix. The first element of each row is the diagonal component of the D matrix. The following elements are the elements next to the diagonal in the L* matrix (the diagonal components in L* are 1). For efficiency it mutates the matrix inplace.

lsqSolve

Arguments

:: (Fractional a, Unbox a)

=> SparseMatrix a

sparse matrix

-> Vector a

Right hand side vector.

-> Vector a

Solution vector

lsqSolve rowStart M y Find a least squares solution x to the system xM = y.

solveTriDiagonal :: (Unbox a, Fractional a) => (a, a, a) -> Vector (a, a, a, a) -> Vector a

solve a tridiagonal system. see metafont the program: ¶ 283

solveCyclicTriD :: (Unbox a, Fractional a) => Vector (a, a, a, a) -> Vector a

solve a cyclic tridiagonal system. see metafont the program: ¶ 286