cubicbezier-0.6.0.3: Efficient manipulating of 2D cubic bezier curves.

Geom2D.CubicBezier.Numeric

Description

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

Synopsis

# Documentation

quadraticRoot :: Double -> Double -> Double -> [Double] Source #

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.

cubicRootNorm :: Double -> Double -> Double -> [Double] Source #

Find real roots from the normalized cubic equation.

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

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 Source #

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.

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

Multiply the vector by the transpose of the sparse matrix.

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

Sparse matrix * vector multiplication.

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

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

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.

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 Source #

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.

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 Source #

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

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

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