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FairCurveModeler
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Modeling curves

Command:  V_Model
Selected geometrical objects 
1. 3d polyline
2. NURBzS curve
3. NURBS curve

 

Command: V_Model

Select object (3D- polyline/mesh/spline-curve/spline-surface): (select object)

Selected geometrical objects:

1. 3d polyline

Selected object - 3d polyline. 
Command line: Enter an option [Setvars/Edvrtxs/Crtscrv/Tonet/eXit]: (enter an option)

Options:

1.1. Setvars – specifies type of 3d polyline and boundary parameters;
1.2. Edtvtxs – edits 3d polyline and simulates creation of v-curves  with 
curvature control;
1.3. Crtscrv – creates v-curve;
1.4. Tonet – unites 3d polylines to net

1.1. Setvars

defines type of polyline and specifies parameters.

Command line: Specify type of polyline [Incpllne/Tngpllne/Splframe/eXit]: (enter an option)

Опции:
1.1.1. Incpllne– defines polyline type as coincidence polyline and specifies boundary parameters
1.1.2. Tngpllne- defines polyline type as tangent polyline and specifies boundary parameters
1.1.3. Splframe - defines polyline type as control polygon and specifies parameters

 

 

1.1.1. Incpllne

defines polyline type as coincidence polyline and specifies boundary parameters.
Command line: Enter an option [Tang/Curvatre/Objects/Arrange/eXit]:(enter an option)

Options:
Tang – specifies tangents in start and last points of a curve.
Specifies tangent in start point
Start tangent? [Yes/No]
: (enter y/n)
Specify tangent: (specify a point)
Specifies tangent in end point
End tangent? [Yes/No]
: (enter y/n)
Specify tangent: (specify a point)

Curvatre – specifies curvature value in first and last points of polyline.
Specifies curvature value in start point
Curvature in start point? [Yes/No]
: (enter y/n)
Specify curvature: (specify positive value)
Specifies curvature value in endpoint
Curvature in endpoint? [Yes/No]
: (enter y/n)
Specify curvature: (specify positive value)

Objects – specifies endpoint tangents and curvatures in accordance with selected circle or 3d line (one segment of 3d polyline). The endpoint coincides with selected circle or line.
Specifies curvature value and tangent in start point
For start tangent select object [Circle / 3d-polyline (1 segm)]
: (select object – circle or line)
For start curvature select object [Circle / 3d-polyline (1 segm)]
: (select object – circle or line)
Specifies curvature value and tangent in endpoint
For last tangent select object [Circle / 3d-polyline (1 segm)]
: (select object – a circle or 3d line)
For last curvature select object [Circle / 3d-polyline (1 segm)]
: (select object – a circle or 3d line)
Arrange – (0 – switch off arrangement, 1 – arranges the points on curve with density proportional to curvature value).



 

1.1.2. Tngpllne


specifies 3d polyline as tangent polyline and specifies boundary parameters

Object – closed 3d polyline
Command line: Enter an option [Fixpnt/eXit]: (enter an option)

Object – unclosed 3d polyline
Command line: Enter an option [Curvatre/ Objects / eXit]: (enter an option)

Options:
Fixpnt – fixes point of contact on closing segment of closed tangent polyline.
Specifies ratio 0 < t < 1 of pieces divided by fix point on closing segment 0 < t = a / (a + b) < 1, a – distance from start point of segment, (a + b ) – length of segment.
The ratio of pieces on closing segment for u (0 < t < 1)
Enter the ratio <0.5>: (enter value)

Curvatre – specifies curvature value in first and last points of polyline.
Specifies curvature value in start point
Curvature in start point? [Yes/No]
: (enter y/n)
Specify curvature: (specify positive value)
Specifies curvature value in endpoint
Curvature in endpoint? [Yes/No]
: (enter y/n)
Specify curvature: (specify positive value)

Objects – specifies endpoint tangents and curvatures in accordance with selected circle or 3d line (one segment of 3d polyline). The endpoint coincides with selected circle or line.
Specifies curvature value and tangent in start point
For start tangent select object [Circle / 3d-polyline (1 segm)]
: (select object – circle or line)
For start curvature select object [Circle / 3d-polyline (1 segm)]
: (select object – circle or line)
Specifies curvature value and tangent in endpoint
For last tangent select object [Circle / 3d-polyline (1 segm)]
: (select object – a circle or 3d line)
For last curvature select object [Circle / 3d-polyline (1 segm)]
: >: (select object – a circle or 3d line)

 

1.1.3. Splframe


specifies 3d polyline as control polygon
Command line: Enter an option [Order/Format/eXit]: (enter an option)

Options:
Format – defines the type of spline control polygon (1 – s-polygon of b-spline curve in "float” format, 2 – sb-polygon in "similar to Bezier polygon” format, 3 – Bezier spline b- polygon, 4 – b-polygon of Bezier curve).
Command line: Specify format of polygons [1 - float s-plg, 2 - sb-plg, 3 - spline b- plg, 4- b-plg] <3>: (enter value).
Order – defines degree of spline curve. Degree m of curve must be in accordance with type of spline curve and number n of polygon vertexes. For unclosed b-spline curve: m <= n /2. For closed b-spline curve: m <= n – 1. For Bezier spline curve: k = (n – 1)/m – is integer, k – number of segments of Bezier spline curve.


 

1.2. Edtvtxs


edits v-curve on 3d polyline / b-spline curve on s-polygon / NURBzS curve on b-polygon curvature with control
Command line: Enter an option [Next/Prev/nUmpoz/setMorfing/incRmove/Setxyz/Fixdir/Clsopn/DEl/Ins ert/STraight/invertGd/VIewcvt/Zconst/eXit]: (enter option)

Options:
Next – moves selection to the next point;
Prev – moves selection to the previous point;
nUmpoz – sets selection to the point under number you specify;

setMorfing – specifies a mode of a type of deformation of a site of a polyline;
Sets a deformable site, starting from the current cursor position.
Define site ...
Specify Position [Prev/Next/numpozU/eXit]: (specify a site of a polyline)

Defines a mode of deformation of a site: simple moving of a site or morfing.
Set Morfing mode for Form Curves (1 - moving , 2 - morfing)<0>: (specify mode)

For morfing uses bell-shaped function. An interval of change of a variable t [0,1], an interval of change of function f (t) [0,1]. The maximal value of function f (0.5) = 1. Zero values of a derivative f ’ (0) = 0, f ’ (0.5) = 0, f ’ (1) = 0.
The subinterval [t0, t1] changes of function морфинга 0 <= t0
If t0> 0 it is possible "to fix" an index point of an interval or to resolve moving an index point.
Enter start point of interval [0,1] <0>: (enter start point)
Enter end point of interval [0,1] <1>: (enter start point)
Sets a mode of deformation of an index point of an interval: 0 - the point does not move, 1 - the point moves.
Is morfing start point? [0 - not morfing, 1 - morfing]<0>: (enter an option)

Setxyz – moves the selected point to the new location you specify.
Fixpnt - for a v-curve on link of inflection of a tangent polyline fixes a point of a contact. Keeps a continuity of curvature, but worsens quality of smoothness.
Fixdir - fixes current point as a point of inflection and sets a tangent.
Clsopn – closes an open polyline, opens a closed polyline.
Del – removes points from a polyline.
Insert – inserts a point.
Straight – straighten a site of a polyline. The rectilinear site of a polyline defines rectilinear site of a curve.
invertGd - changes a geometrical determinant of a v-curve (the coincidece polyline is replaced with a tangent polyline). The curve does not vary.
VIewcvt – sets a mode of displaying of the curve of curvature.
Zconst – (0 – switches off, 1 - switches on an option of preservation of coordinate Z at moving a point).

incRmove - moves the selected point to the new location in incremental mode (by increments). One pressing of key ENTER causes moving a point on one small increment. Originally the vector of an increment is directed on a median of the triangle made of the previous point, the current point, the next point. Originally the size of a vector is equal 1/100 sizes of a median.
Command: Enter an option [Move/setStep/setDir/seeCurve/seeRads/seecVtre/scAle/exitUndo/eXitfix]
: (enter an option)
Options:
Move – moves a point on a vector of increment.
setStep – redefines a step of incremental moving (size of a vector of an increment).
setDir – redefines a direction of incremental moving (the vector of an increment).
seeCurve – displays only a curve.
seeRads – displays a curve of the centers of curvature.
seecVtre – displays a curve of curvature.
scALe – specifies scale factor for curvature.
exitUndo – exits without preservation of changes.
eXitfix – exits with preservation of changes.



 

1.3. Crtscrv


creates a v-curve on a 3d polyline. Approximates v-curve by cubic NURBzS model.


 

1.4. Tonet

Tonet – unites 3d polylines to set.
Command: Add/Undo/eXit:(enter an option)
Add – adds polyline to set.
Undo – removes the last polyline.
eXit – exit.


 

2. NURBzS curve


Selected object - cubic NURBzS curve.

Command: Enter an option [Setvars/BSpline/Formbs/exTRact/Multiply/eLevate/Viewcvt/TEstb/Break/cRvsrf/eXit]: (enter an option)

Selected object - NURBzS curve of degree > 3.
Command: Enter an option [Setvars/Formbs/exTRact/Multiply/eLevate/Viewcvt/TEstb/Break/cRvsrf/eXit]:(enter an option)

Options:
2.1. Setvars – specifies parameters.
2.2. BSpline – creates b-spline curve on v- curve presented by cubic NURBzS-model.
2.3. Formbs – converts b-polygon in s- polygon.
2.4. exTRact - allocates a part of a curve.
2.5. Multiply – increases the number of control points uniformly across the spline for more localized control. The type of curve and degree do not vary.
2.6. Elevate – elevates the cubic degree of NURBzS curve up to 6 with smoothing of spatial curve twist.
2.7. Viewcvt – displays curves of curvature
2.8. TEstb – specifies the end parameters of the curve.
2.9. Break – breaks primitive on a polyline of the interpolated points and polyline of control points.
2.10. Crvsrf - unites curves to the set of curves. Polylines of nodes are united in 3d mesh – carrier of set of curves.


 

2.1. Setvars

specifies parameters.

Command line: Enter an option [segmU/Frame/Viewcvt/FAiring/eXit]: (enter an option)

For NURBzS curve of any degree. Enter an option [segmU/Viewcvt/eXit]:

Options:
segmU – specifies number of lines approximated one segment of spline curve.
Enter number of segments<8>(enter a number)
Viewcvt – specifies options to display curvature graph.
Enter an option for curvature graph [0 - Radiuses / 1 - Curvature ] <0>: (enter an option)
Enter a scale with sign for curvature < -0.25>: (enter a value) Sets the maximal ordinate of curvature concerning from length of a curve. At negative value of option the curvature graph is postponed from the opposite side of a curve from the evolute fraph.
Fairing – displays or not displays the control polygon.
Enter fairing option for curves [0 - off / 1 - on] <0>: (enter an option)


 

2.2. BSpline


creates b-spline curve on v-curve presented by cubic NURBzS-model.
Enter degree for b-spline <8>:(enter degree m: 4 <= m <= 10)


 

2.3. Formbs


Converts b-polygon to s-polygon. If the NURBzS curve has been received by subdividing of one segment of a NURBzS curve or converting of a NURBS curve in format the NURBzS curve does not vary.
Generally the new curve curve does not coincide with an initial curve. Keeps boundary points and curvature in boundary points.



 

2.4. exTRact


allocates a part of a curve.


 

2.5. Multiply


sudivides the specification of a curve. Increases quantity of control points. The type of a curve and a degree do not change.

 

2.6. Elevate


elevates degree of a NURBzS curve on 1. The degree of a cubic NURBzS curve elevates up to 6-th with smoothing of torsion of a spatial curve. 
< /not>
If you answer 'yes' to the request
'Are realy points on Ellipse / Circle [0 - not one - yes] <0>:'
program converts the geometric NURBzS  curve to real spline NURBzS curve. Then real spline NURBzS  curve can be transformed to a rational NURBS curve in the format of b- spline curve geometrically precise approximating ellipse.


 

2.7. Viewcvt


Viewcvt – specifies options to display curvature graph.
Enter an option for curvature graph [0 - Radiuses / 1 - Curvature ] <0>: (enter an option)
Enter a scale with sign for curvature < -0.25>: (enter a value) Sets the maximal ordinate of curvature concerning from length of a curve. At negative value of option the curvature graph is postponed from the opposite side of a curve from the evolute graph.

2.8. TEstb


This option specifies the end parameters of the curve as the tangent segments of 3D Polyline and the circles.

2.8. Break


breaks primitive on a polyline of the interpolated points and a polyline of control points (a kind of "float s- polygon" or "clamped s-polygon").

 

2.9. Crvsrf

unites curves to the set of curves. Polylines of nodes NURBzS curves / s-polygons of b-spline curves are united in 3d mesh – carrier of set of curves.
Enter an option [Add/Undo/Close/eXit]: (enter an option)
Параметры:
Add – selects and adds another curve.
Select curve line: (select object)
Close – closes the 3d mesh carrier
Undo – cancels of last selection.



 

3. NURBS curve.

Selected object - NURBS curve.
Command line: Enter an option [Setvars/Edvrtxs/Formbz/exTRact/Multiply/Viewcvt/TEstb/Break/cRvsrf/eXit]:(enter an option)
Options:
3.1. Setvars – sets parameters of a curve.
3.2. Edtvtxs – edits a curve with testing curvature.
3.3. Formbz – transforms a format of a curve to format NURBzS curve.
3.4. Multiply – sudivides the specification of a curve.
3.5. Viewcvt – shows curvature
3.6. TEstb – specifies the end parameters of the curve.
3.7. Break – breaks primitive on a polyline of the interpolated points and a polyline of control points (a kind of "float” s-polygon or clamped s-polygon).
3.8. Crvsrf – unites curves to the set, s-polygons of curves to the network carrier. On 4-th boundary NURBS curves forms a NURBS surface under Coons formula.


 

3.1. Setvars


sets parameters of a curve.
Command line: Enter an option [segmU/Frame/Viewcvt/eXit]: (enter an option)
Options:
segmU – specifies number of lines approximated one segment of spline curve.
Enter number of segments<8>(enter number)
Frame – defines type of s-polygon for editing: "float" or "clamped".
Specify polygon type for editing [0 - clamped, 1 - float] <0>: (define type)
Viewcvt – specifies options to display curvature graph.
Enter an option for curvature graph [0 - Radiuses / 1 - Curvature ] <0>: (enter an option)
Enter a scale with sign for curvature < -0.25>: (enter a value) Sets the maximal ordinate of curvature concerning from length of a curve. At negative value of option the curvature graph is postponed from the opposite side of a curve from the evolute graph.


 

3.2. Edtvtxs

edits NURBS curve with testing curvature
Command Line:
Enter an option [Next/Prev/nUmpoz/setMorfing/pnmoVe/incRmove/Setxyz/Addknot/setRAdius/ Weight/STraight/VIewcvt/Zconst/eXit]: (enter an option)
Options: 
< /no>
Addknot - adds a new node point. Divides the current segment of the spline in half.
Weight – sets weight of the current control point.
setRAdius - sets new values of curvature in boundary points of a curve.
Preliminary it is necessary to set an option of display of curvature. Otherwise gives out the message
*** Switch on option to display Curvature or Radius
Requests a point on a curve and the center of curvature or a point of curvature:
Set point on curve:(specify a point on a curve)
Set new centre:(Specify the new center of curvature or a point of curvature)
Other options of editing of s-polygon as are given to a polyline in Edtvrtxs


 

3.3. Formbz

transforms a format of a NURBS curve to format NURBzS curve;

 

3.4. Multiply

sudivides the specification of a curve.

 

3.5. Viewcvt

specifies options to display curvature graph.
Enter an option for curvature graph [0 - Radiuses / 1 - Curvature ] <0>: (enter an option)
Enter a scale with sign for curvature < -0.25>: (enter a value) Sets the maximal ordinate of curvature concerning from length of a curve. At negative value of option the curvature graph is postponed from the opposite side of a curve from the evolute graph.

3.6. TEstb

specifies the end parameters of the curve as the tangent segments of 3D Polyline and the circles

 

3.7. Break

breaks primitive on a polyline of the interpolated points and a polyline of control points (a kind of "float” s-polygon or clamped s-polygon)

 

3.8. Crvsrf

Option Tonet: 
unites curves to the frame. Base node polylines of NURBzS curves / s-polygons of b-spline curves unites the network carrier.
Command line: 
For set of polygons/curves n = ...
Enter an option [Add/Undo/Close/eXit]: (enter option)
Options:
Add – selects and adds another curve.
Select curve line: (select object)
Close – closes the 3d mesh carrier.
Undo – cancels of last selection.
 
Option Toedgs:
on four boundary NURBS-curves forms a NURBS-surface Command line:
Select curve 2 for surface edge: (select 2-nd curve)
Select curve 3 for surface edge: (select 3-d curve)
Select curve 4 for surface edge: (select 4-th curve)
Boundary curves are specified consistently, bypassing a contour on hour or counter-clockwise.

 

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