Parametric curve evaluation method and apparatus for a computer graphics display system

Apparatus for converting non-uniform rational b-spline (NURBS) data representative of a parametric curve to geometric coordinates for subsequent rendering and display by a computer graphics system, said curve having parameter points (t) therealong and comprising successive spans, each span being defined by control points and knot values, said NURBS data including control point data defining said control points and a knot vector defining said knot values, said apparatus comprising:

• first memory means (12) for storing NURBS data defining successive spans of said curve as a sequence of data records such that each successive span of the curve is defined by a corresponding individual data record in conjunction with a predetermined number of immediately preceding data records of the sequence;
• a graphics control processor (14) for converting said control point data to homogeneous coordinates (wx, wy, wz, w) to generate converted control point data;
• second memory means (39, 49, 57x-57w), having a plurality of rows including a first row, for storing the NURBS data defining a particular span, said second memory means being updated for a new span by storing new data in said first row and shifting previously stored data into a subsequent row, said graphics control processor processing NURBS data stored in said second memory means;
• means for transferring said data records from said first memory means to said second memory means for processing by said graphics control processor, said transferring means being initially operable to transfer the data records defining the first span of said curve from said first memory means to said second memory means for determination of the coordinates of the parameter points along said first span and being subsequently operable to transfer an additional data record from said first memory means to said second memory means for determination of the coordinates of the parameter points along each additional span;
• a plurality of parallel floating point processors (16x, 16y, 16z, 16w), corresponding respectively to said homogeneous coordinates, for receiving said converted control point data and for simultaneously determining the homogeneous coordinates of said curve at each of said parameter points along the curve to produce outputs (wx(t), wy(t), wz(t), w(t)) representing said coordinates at said points, each of said processors determining the corresponding homogeneous coordinate of said curve at each of said parameter points;
• and
• a further floating point processor (18) for receiving the outputs of the parallel floating point processors and converting said outputs to geometric coordinates (x, y, z) of said parameter points for subsequent rendering and display of the curve by said graphics system.

Apparatus for converting non-uniform rational b-spline (NURBS) data representative of a parametric curve to geometric coordinates for subsequent rendering and display by a computer graphics system, said curve having parameter points (t) therealong and comprising one or more spans, each span being defined by control points and knot values, said NURBS data including control point data defining said control points and a knot vector defining said knot values, said apparatus comprising:

• a graphics control processor (14) for transforming said control point data from modelling coordinates to view coordinates to generate transformed control point data and for converting said transformed control point data to homogeneous coordinates (wx, wy, wz, w) to generate converted control point data;
• a plurality of parallel floating point processors (16x, 16y, 16z, 16w), corresponding respectively to said homogeneous coordinates, for receiving said converted control point data and for simultaneously determining the homogeneous coordinates of said curve at each of said parameter points along the curve to produce outputs (wx(t), wy(t), wz(t), w(t)) representing said coordinates at said points, each of said processors determining the corresponding homogeneous coordinate of said curve at each of said parameter points;
• and
• a further floating point processor (18) for receiving the outputs of the parallel floating point processors and converting said outputs to geometric coordinates (x, y, z,) of said parameter points for subsequent rendering and display of the curve by said graphics system.

Apparatus for converting non-uniform rational b-spline (NURBS) data representative of a parametric curve to geometric coordinates for subsequent rendering and display by a computer graphics system, said curve having parameter points (t) therealong and comprising one or more spans, each span being defined by control points and knot values, said NURBS data including control point data defining said control points and a knot vector defining said knot values, said apparatus comprising:

• a graphics control processor (14) for converting said control point data to homogeneous coordinates (wx, wy, wz, w) to generate converted control point data;
• a plurality of parallel floating point processors (16x, 16y, 16z, 16w), corresponding respectively to said homogeneous coordinates, for receiving said converted control point data and for simultaneously determining the homogeneous coordinates of said curve at each of said parameter points along the curve to produce outputs (wx(t), wy(t), wz(t), w(t)) representing said coordinates at said points, said parameter points being generated by said graphics control processor and transmitted to said parallel floating point processors, each of said processors determining the corresponding homogeneous coordinate of said curve at each of said parameter points;
• and
• a further floating point processor (18) for receiving the outputs of the parallel floating point processors and converting said outputs to geometric coordinates of said parameter points for subsequent rendering and display of the curve by said graphics system.

Apparatus for converting non-uniform rational b-spline (NURBS) data representative of a parametric curve to geometric coordinates for subsequent rendering and display by a computer graphics system, said curve having parameter points (t) therealong and comprising one or more spans, each span being defined by control points and knot values, said NURBS data including control point data defining said control points and a knot vector defining said knot values, said apparatus comprising:

• a graphics control processor (14) for converting said control point data to homogeneous coordinates (wx, wy, wz, w) to generate converted control point data;
• a plurality of parallel floating point processors (16w, 16x, 16y, 16z), corresponding respectively to said homogeneous coordinates, for receiving said converted control point data and for simultaneously determining the homogeneous coordinates of said curve at each of said parameter points along the curve to produce outputs (wx(t), wy(t), wz(t), w(t)) representing said coordinates at said points, each of said processors determining the corresponding homogeneous coordinate of said curve at each of said parameter points, one of said parallel floating point processors (16w) providing an output (w(t)) representative of a weight for each of said parameter points;
• and
• a further floating point processor (18) for receiving the outputs of the parallel floating point processors and converting said outputs to geometric coordinates (x, y, z) of said parameter points for subsequent rendering and display of the curve by said graphics system, said further floating point processor inverting said output of said one parallel floating point processor to obtain the reciprocal of said output and multiplying the outputs of the other parallel floating point processors by said reciprocal to obtain said geometric coordinates.

A method of converting non-uniform rational b-spline (NURBS) data representative of a parametric curve to geometric coordinates for subsequent rendering and display by a computer graphics system, said curve comprising successive spans with parameter points along said spans, said method comprising the steps of:

• storing said NURBS data in a first memory means as a sequence of data records such that each successive span of the curve is defined by a corresponding individual data record in conjunction with a predetermined number of immediately preceding data records of the sequence;
• initially transferring the data records defining the first span of said curve from said first memory means to a second memory means and determining the coordinates of the parameter points along said first span of said curve from the data records initially transferred to said second memory means;
• for each successive span of said curve following said first span, transferring an additional data record from said first memory means to said second memory means and determining the coordinates of the parameter points along said span of said curve from said additional data record in conjunction with the data records previously transferred to said second memory means;
• and
• generating a straight line segment for each said span of said curve from said coordinates corresponding to said parameter points along each said span.

Apparatus for converting non-uniform rational b-spline (NURBS) data representative of a parametric curve to geometric coordinates for subsequent rendering and display by a computer graphics system, said curve comprising successive spans with parameter points along said spans, said apparatus comprising:

• a RAM for storing NURBS data defining said curve as a sequence of data records such that each successive span of the curve is defined by a corresponding individual data record in conjunction with a predetermined number of immediately preceding data records of the sequence;
• processing means for determining the coordinates of the parameter points along a particular span of said curve, said processing means having memory means associated therewith for storing NURBS data defining said span of said curve;
• and
• means for transferring said data records from said RAM to said memory means for determination of the coordinates of said parameter points by said processing means, said transferring means initially transferring the data records defining the first span of said curve from said RAM to said memory means for determination of the coordinates of the parameter points along said first span and subsequently transferring an additional data record from said RAM to said memory means for determination of the coordinates of the parameter points along each additional span.