KNOT_VECTORS(3G)

NAME

default_knots, u_knot_vector, v_knot_vector − define knot vector(s) for drawing subsequent space curves or surfaces

SYNOPSIS

C Syntax:

void default_knots (fildes);
int fildes;

void u_knot_vector(fildes, knot_vector, numpts);
int fildes, numpts;
float knot_vector[];

void v_knot_vector(fildes, knot_vector, numpts);
int fildes, numpts;
float knot_vector[];

FORTRAN77 Syntax:

subroutine default_knots(fildes)
integer*4 fildes

subroutine u_knot_vector(fildes,knot_vector,numpts)
integer*4 fildes,numpts
real knot_vector()

subroutine v_knot_vector(fildes,knot_vector,numpts)
integer*4 fildes,numpts
real knot_vector()

Pascal Syntax:

procedure default_knots(fildes:integer);

procedure u_knot_vector(fildes:integer;
var knot_vector:array[lo..hi:integer] of real;
numpts:integer);

procedure v_knot_vector(fildes:integer;
var knot_vector:array[lo..hi:integer] of real;
numpts:integer);

DESCRIPTION

Input Parameters

fildes Integer file descriptor returned by gopen when an I/O path to a graphics device is opened.

knot_vector Vector defining the knots to be used in the processing of spline curves and surfaces.

numpts Number of entries in the knot vector.

Discussion

U_knot_vector and v_knot_vector specify the knot vectors to be used with subsequent trimming_curve, spline_curve, and spline_surface procedures. Default_knots specifies that uniform (1.0 spacing), non-multiple knots are to be used. The first interval used in rendering the spline will be 0 to 1. This is a faster method of interpolating, because it is not necessary to recompute basis matrices for each knot sequence. These knot vectors are used in calculating basis matrices used for interpolating spline curves and surfaces.

For trimming curves and spline curves, only the u knot vector is used. Knot vector routines can also handle non-uniform splines, so knot vectors are not restricted to integer values. They can also start at values other than 0.0.

DEFAULTS

Uniform (1.0 spacing) non-multiple knots, giving the following basis matrices:

Cubic u and v basis matrices:

          | -1.0 3.0 -3.0 1.0 |                 | -1.0 3.0 -3.0 1.0 |
      1/6| 3.0 -6.0 3.0 0.0 |              1/6| 3.0 -6.0 0.0 4.0 |
         | -3.0 3.0 3.0 0.0 |                 | -3.0 3.0 3.0 1.0 |
         | 1.0 4.0 1.0 0.0 |                 | 1.0 0.0 0.0 0.0 |

Quadratic u and v basis matrices:

           | 0.5 -1.0 0.5 |                 | 0.5 -1.0 0.5 |
          | -1.0 1.0 0.0 |                 | -1.0 1.0 0.5 |
          | 0.5 0.5 0.0 |                 | 0.5 0.0 0.0 |

Linear u and v basis matrices:

| -1.0 1.0 | | -1.0 1.0 |
| 1.0 0.0 | | 1.0 0.0 |

which are the b-spline basis matrices.

Museum