Parametric curve

The parametric-curve library provides an implementation of parametric curves. Parametric curves are n-dimensional curves described by parametric equations, one per each dimension. For example:

 x = a cos (t)
 y = a sin (t)
 z = bt

In this example, t is the parameter, and a and b are constants.

  1. Parametric curve
  2. Usage
  3. Documentation
    1. Procedures
  4. Examples
  5. About this egg
    1. Author
    2. Version history
    3. License

Usage

(require-extension parametric-curve)

Documentation

Procedures

[procedure] parametric-curve? :: OBJECT -> BOOL

Returns #t if the given object is a parametric curve, #f otherwise.

[procedure] simple-curve :: N * K * FS * TMIN * TMAX -> PCURVE

Basic parametric curve constructor.

N
number of interpolation points (N >= 3)
K
continuity class of the interpolating spline for this curve (1 or 2, for first or second derivative)
FS
a list of one-argument procedures that are evaluated to obtain points on the curve. The length of FS determines the dimensionality of the curve
TMIN
minimum value for the curve parameter
TMIN
maximum value for the curve parameter
[procedure] sample-curve :: PCURVE -> (T -> POINT)

Constructs a procedure to sample the curve at the given parameter value.

[procedure] sample-curve* :: PCURVE -> (T LIST -> POINT LIST)

Constructs a procedure to sample the curve at the given parameter values.

[procedure] linear-curve :: N * COEFFS * TMIN * TMAX -> PCURVE

Constructor for a linear curve of the form c1 * x + c2.

N
number of interpolation points (N >= 3)
COEFFS
supplies c1 and c2 for the different dimensions
TMIN
minimum value for the curve parameter
TMAX
maximum value for the curve parameter
[procedure] line-segment:: N * COEFFS -> PCURVE

Creates a line segment whose starting point is zero, and its end points is defined by COEFFS. N is the number of interpolating points.

[procedure] map-curve :: FS * PCURVE -> PCURVE

Maps the given functions to the parametric curve.

[procedure] iterate-curve :: PCURVE * N -> POINT LIST

Samples a parametric curve at N regular intervals in the range xmin..xmax inclusive.

[procedure] range-curve :: PCURVE * N * (X1,XN) LIST -> POINT LIST

Samples a parametric curve at regular intervals in the given ranges.

[procedure] arc-length :: PCURVE * DX -> NUMBER

Computers the arc length of the curve given step DX.

Examples

About this egg

Author

Ivan Raikov.

Version history

1.7
Added arc-length
1.4
Added line-segment
1.0
Initial release

License

Copyright 2012-2014 Ivan Raikov and the Okinawa Institute of Science and Technology

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or (at
your option) any later version.

This program is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
General Public License for more details.

A full copy of the GPL license can be found at
<http://www.gnu.org/licenses/>.