Miscellaneous Submodules

klampt.math.geodesic module

class klampt.math.geodesic.CartesianSpace(d)

Bases: klampt.math.geodesic.GeodesicSpace

The standard geodesic on R^d

extrinsicDimension()

intrinsicDimension()

class klampt.math.geodesic.GeodesicSpace

A class representing a geodesic space. A geodesic is equipped with a a geodesic (interpolation via the interpolate(a,b,u) method), a natural arc length distance metric (distance(a,b) method), an intrinsic dimension (intrinsicDimension() method), an extrinsic dimension (extrinsicDimension() method), and natural tangents (the difference and integrate methods).

difference(a, b)

For Lie groups, returns a difference vector that, when integrated would get to a from b. In Cartesian spaces it is a-b.

distance(a, b)

extrinsicDimension()

integrate(x, d)

For Lie groups, returns the point that would be arrived at via integrating the difference vector d starting from x. Must satisfy the relationship a = integrate(b,difference(a,b)). In Cartesian spaces it is x+d

interpolate(a, b, u)

intrinsicDimension()

class klampt.math.geodesic.MultiGeodesicSpace(*components)

This forms the cartesian product of one or more GeodesicSpace’s. Distances are simply added together.

difference(a, b)

distance(a, b)

extrinsicDimension()

integrate(x, diff)

interpolate(a, b, u)

intrinsicDimension()

join(xs)

split(x)

class klampt.math.geodesic.SE3Space

Bases: klampt.math.geodesic.GeodesicSpace

difference(a, b)

distance(a, b)

extrinsicDimension()

integrate(x, d)

interpolate(a, b, u)

intrinsicDimension()

class klampt.math.geodesic.SO2Space

Bases: klampt.math.geodesic.GeodesicSpace

difference(a, b)

distance(a, b)

extrinsicDimension()

integrate(x, d)

interpolate(a, b, u)

intrinsicDimension()

class klampt.math.geodesic.SO3Space

Bases: klampt.math.geodesic.GeodesicSpace

difference(a, b)

distance(a, b)

extrinsicDimension()

integrate(x, d)

interpolate(a, b, u)

intrinsicDimension()

klampt.math.spline module

Spline utilities.

klampt.math.spline.bezier_discretize(x1, x2, x3, x4, res, return_params=False)

Discretizes a bezier curve into a list of points. If return_params is True, a pair (points,params) is returned where params are the exact parameter values for which each point was generated. Otherwise, just the points are returned.

klampt.math.spline.bezier_length_bound(x1, x2, x3, x4)

Returns an upper bound on the arc length of the bezier curve

klampt.math.spline.bezier_subdivide(x1, x2, x3, x4, u=0.5)

Subdivides a Bezier curve at the parameter u

klampt.math.spline.bezier_to_hermite(x1, x2, x3, x4)

Returns the cubic bezier representation of a hermite curve

klampt.math.spline.hermite_deriv(x1, v1, x2, v2, u, order=1)

Returns the derivative of a hermite curve with control points x1, v1, x2, v2 at the parameter u in [0,1]. If order > 1, higher order derivatives are returned.

klampt.math.spline.hermite_eval(x1, v1, x2, v2, u)

Returns the position a hermite curve with control points x1, v1, x2, v2 at the parameter u in [0,1].

klampt.math.spline.hermite_length_bound(x1, v1, x2, v2)

Returns an upper bound on the arc length of the hermite curve

klampt.math.spline.hermite_subdivide(x1, v1, x2, v2, u=0.5)

Subdivides a hermite curve into two hermite curves.

klampt.math.spline.hermite_to_bezier(x1, v1, x2, v2)

Returns the cubic bezier representation of a hermite curve