Example:

point p1 (-1 -1 0) endpoint point p2 (-2 0 0) endpoint point p3 (-1 1 0) endpoint point p4 ( 0 0 0) endpoint point p5 ( 1 -1 0) endpoint point p6 ( 2 0 0) endpoint point p7 ( 1 1 0) endpoint controlpoint cp1 point p1 endcontrolpoint controlpoint cp5 point p5 endcontrolpoint		B-spline curve with yellow control polygon
bsplinecurve id   order 4 controlpointlist (cp1 p2 p3 p4 cp5 p6 p7) slices 30 drawcontrols 1 endbsplinecurve

beziercurve

A beziercurve statement describes a surface that interpolates the end points and approximates the other points defined by the controlpoint_idlist (which contains either points or controlpoints). A beziercurve can be used as a sweep path, sweepmorph path, or crosssection.

The dynamic values are: slices_int and the points in the controlpoint_idlist.

The beziercurve parameters have the following constraints:

Example:

point p1 (-1.5 -0.5 0) endpoint point p2 (-0.5 0.5 0) endpoint point p3 ( 0.5 0.5 0) endpoint point p4 ( 1.5 -0.5 0) endpoint controlpoint cp3 point p3 endcontrolpoint		Bezier curve with yellow control polygon
beziercurve id   controlpointlist (p1 p2 cp3 p4) drawcontrols1 endbeziercurve

polyline

A polyline statement describes 3D piecewise linear segments. There must be atleast 2 points in the pointlist (which contains either points or controlpoints). A polyline can be used as a sweep path, sweepmorph path, or crosssection.

Field	Description
pointlist	A list containing points or controlpoints. The length of this list must be atleast 2.
drawpoints	Boolean that specifies whether or not to draw the points.

Example:

point p1 (-2.0 -2.0 0.0) endpoint point p2 ( 1.0 1.0 0.0) endpoint point p3 ( 2.0 -1.0 0.0) endpoint point p4 ( 0.0 -1.0 0.0) endpoint point p5 ( 3.0 1.0 0.0) endpoint controlpoint cp1 point p1 endcontrolpoint		line segments with points drawn
polyline id   pointlist (cp1 p2 p3 p4 p5) drawpoints 1 endpolyline

crosssection

A crosssection is a polyline, usually 2D and defined in the xy-plane, but can be three dimensional. A crosssection can be used by itself or in conjunction with a sweep or sweepmorph.

There are 6 crosssection types:

crosssection id type polyline id endcrosssection		Reference to a polyline.
crosssection id type beziercurve id endcrosssection		Reference to a beziercurve.
crosssection id type bsplinecurve id endcrosssection		Reference to a bsplinecurve.
crosssection id type circle radius radius_float slices slices_int endcrosssection		A circle with slices_int sides. radius > 0 slices >= 3
crosssection id type cresent radius radius_float theta theta_float thickness thickness_float slices slices_int endcrosssection		A "C" shape with an arc determined by theta and the radius. radius > 0 theta > 0 thickness > 0 slices >= 1
crosssection id type star innerradius innerradius_float outerradius outerradius_float slices slices_int endcrosssection		A star with slices_int points. innerradius > 0 outerradius > 0 slices >= 2

Example:

crosssection id   type cresent radius 1.0 theta 70 thickness 0.2 slices 10 endcrosssection

sweep

A sweep statement describes the result of sweeping the crosssections along the path. The path must a bsplinecurve, beziercurve, or polyline. Each path has a set of Frenet Frames (tangents, normals, & binormals) that are used to determine how the cross section will twist along the path. The user can control the twist in five ways and these options are additive in the order given below:

1) minimizetorsion - minimizes the twisting of the intrinsic Frenet frame.
2) closed - specifies that the path is closed.
This changes the Frenet frames so that the first and last Frenet frames are aligned using the symmetry of the crosssection. For example, a square has symmetry 4, so when a path is closed the Frenet Frames should be aligned within (360/4)=90 degrees about the tangent.

3) azimuth - angle about the tangent that all Frenet frames will be rotated by.
4) twist - angle about the tangent that specifies the overall amount of twist from the first Frenet frame to the last.
5) warp - sets each scale and twist angle explicitly:

In the path controlpoints the scale and rotate values transform the crosssection in the Frenet Frame coordinate system. (x y z) correspond to the Frenet Frame (normal, binormal, tangent), which are drawn in (red, green, blue).

Example:

crosssection csCircle   type circle radius 0.25 slices 20 endcrosssection crosssection csStar   type star outerradius 0.70 innerradius 0.35 slices 5 surface sBlue endcrosssection point p1 ( -4.0 4.0 0.0) endpoint point p2 ( 4.0 4.0 0.0) endpoint point p3 ( 4.0 -4.0 0.0) endpoint point p4 ( -4.0 -4.0 0.0) endpoint beziercurve bz   controlpointlist (p1 p2 p3 p4) drawcontrols 1 endbeziercurve sweep sw   path bz minimizetorsion 1 endpath crosssection csCircle surface sRed endcrosssection crosssection csStar transform     translate (1.2 0 0) endtransform endcrosssection meshtype SLF_TRIANGLES drawsweep 1 drawpath 0 endsweep

Bezier curve path of the sweep Final swept circle and star

sweepmorph

A sweepmorph is very similar to a sweep. However, instead of specifying crosssections inside the sweepmorph, crosssections are associated with the path controlpoints. Any path controlpoint may have a crosssection reference, but the first and last controlpoint must contain a crosssection reference. The crosssections are linearly interpolated across the path. All crosssections must have the same number of points.

Example:

crosssection cCircle   type circle radius 0.6 slices 22 endcrosssection crosssection cStar   type star outerradius 1.0 innerradius 0.75 slices 11 endcrosssection point p1 (-3.0 0.0 0.0) endpoint point p2 (-1.0 2.0 0.0) endpoint point p3 ( 1.0 2.0 0.0) endpoint point p4 ( 3.0 0.0 1.0) endpoint controlpoint cp1   point p1 crosssection cCircle endcontrolpoint controlpoint cp4   point p4 crosssection cStar endcontrolpoint beziercurve bz   controlpointlist (cp1 p2 p3 cp4) slices 30 drawcontrols 1 endbeziercurve sweepmorph sm   path bz    minimizetorsion 1 endpath begincap 1 endcap 1 drawsweep 1 endsweep

2D crosssections cCircle and cStar The beziercurve path for the sweepmorph The sweepmorph with endcaps

bsplinepatch

A bsplinepatch statement describes a surface that approximates the control mesh defined by the controlpoint_idlist. The surface normals point in the u cross v direction. An offset surface is created if distance_float is non-zero. This surface is connected to the original surface is connected_bool is non-zero.

The bsplinepatch parameters have the following constraints:

The dynamic values are: uslices, vslices, and the controlpointlist points.

Example:

point p0 (1 5 12) endpoint ... point p19 (17 6 -2) endpoint		Connectivety of the control points
bsplinepatch id   uorder 4 uknots 9 uknotlist (0 1 2 3 4 5 6 7 8) vorder 4 vknots 8 vknotlist (2.3 5.1 6.3 6.4 7.2 8.9 9.2 14) controlpointlist (p0   p1   p2  p3   p4                               p5   p6   p7   p8   p9                               p10 p11 p12 p13 p14                               p15 p16 p17 p18 p19)  endbsplinepatch

bezierpatch

A bezierpatch statement describes a surface that interpolates the four corner points of the control mesh and approximates the other points defined by the controlpoint_idlist. The surface normals point in the u cross v direction. An offset surface is created if distance_float is non-zero. This surface is connected to the original surface is connected_bool is non-zero.

The bezierpatch parameters have the following constraints:

The dynamic values are: uslices, vslices, and the controlpointlist points.

Example:

point p0 (-6 4 8) endpoint ... point p11 (2 32 -7) endpoint		Connectivety of the control points
bezierpatch id   uorder 4 vorder 3 controlpointlist (p0  p1  p2   p3                                 p4  p5  p6     p7                                p8  p9  p10  p11) endbezierpatch

nurbpatch

A nurbpatch is rational spline surface based on bsplinepatches The surface normals point in the u cross v direction. An offset surface is created if distance_float is non-zero. This surface is connected to the original surface is connected_bool is non-zero.

The nurbpatch parameters have the following constraints:

The dynamic values are: uslices, vslices, and the controlpointlist points.

Partial Cylinder Example:

point p0 (-2 0 1.0 1.0) endpoint point p1 (-2 0 0.0 1.0) endpoint point p2 (-2 0 -1.0 1.0) endpoint point p3 ({expr -2.0*0.7071} {expr 2.0*0.7071} {expr 1.0*0.7071} {expr 0.7071} ) endpoint point p4 ({expr -2.0*0.7071} {expr 2.0*0.7071} {expr 0.0*0.7071} {expr 0.7071} ) endpoint point p5 ({expr -2.0*0.7071} {expr 2.0*0.7071} {expr -1.0*0.7071} {expr 0.7071} ) endpoint point p6 (0 2 1.0 1.0) endpoint point p7 (0 2 0.0 1.0) endpoint point p8 (0 2 -1.0 1.0) endpoint

nurbpatch id   uorder 3 uknots 6 uknotlist (0 0 0 1 1 1) vorder 3 vknots 6 vknotlist (0 0 0 1 1 1) uslices 20 vslices 20 controlpointlist (p0 p1 p2                               p3 p4 p5                               p6 p7 p8) endnurbpatch

Partial cylinder with texture and normals drawn