Plotting

Summary
Plotting
Functions
Plot2DPlots a system of 2 variables
PlotCurve3DPlots a curve given by implicit equations in 3 variables.
Plot3DPlots a system of 3 variables using maple internal plotting functions.
Plot3DglsurfPlots a system of 3 variables using glsurf.
Plot3DsurfexPlots a system of 3 variables using surfex (software based on surf).
PlotWorkspacePlot the border of a manipulator workspace
ConfigurationsComputes the different possible positions.
PlotRobot2DPlot a planar manipulator
PlotRobot3DPlot a 3D manipulator
PlotCell3DPlot the cells returned CellDecomposition or CellDecompositionPlus
PlotCell2DPlot the cells returned CellDecomposition or CellDecompositionPlus
SetCellColorsSet colors to the numbers of solutions obtained by NumberOfSolutionsPlus
TrajectoryDisplay a given trajectory.
ImageTrajectoryDisplay a given trajectory.

Functions

Plot2D

Plot2D := proc (
   sys ::{algebraic, equation(algebraic), list({algebraic,equation(algebraic), algebraic<algebraic}), list(list({algebraic,equation(algebraic), algebraic<algebraic}))},  
   e1 ::name = range,
   e2 ::name = range,
   {   
   points ::truefalse := false,
   [ notest, draft ] ::truefalse := false
   }   
)

Plots a system of 2 variables

Parameters

sysa list or a list of list of polynomials: the system
v1 = r1v1 is a name of sys and r1 a range of values
v2 = r2v2 is a name of sys and r2 a range of values
points = bool (optional)bool is a boolean: if false, isolated points are ignored; default value: false;
notest = b (optional)b is a boolean; when b is true the inequality and real constraints are ignored; default value: true;
opts (optional)arguments passed to the maple function plots:-implicitplot

Returns

A graphic: the solutions of the system.

  • when sys is a polynomial, the graphic is the zeroes of this polynomial
  • when sys is a list of polynomials [p1,...,pk], the graphic is the zeroes of the system p1=0 and ... and pk=0
  • when sys is a list of list of polynomials [L1,...,Lk], the graphic is the union of the zeroes of each system L1, ..., Lk.

PlotCurve3D

PlotCurve3D := proc (
   sys ::{algebraic, equation(algebraic), list({algebraic,equation(algebraic), algebraic<algebraic}), list(list({algebraic,equation(algebraic), algebraic<algebraic}))},  
   ineq ::list({polynom, polynom<polynom}) := [],
   e1 ::name = range := sort ([op(indets([sys,x,y,z],name))])[1] =-5..5,
   e2 ::name = range := sort ([op(indets([sys,x,y,z],name) minus {lhs(e1)})])[1] =-5..5,
   e3 ::name = range := sort ([op(indets([sys,x,y,z],name) minus {lhs(e1),lhs(e2)})])[1] =-5..5,
   {   
   grid ::integer := 30,
   output ::identical(list,display) := ':-display'
   }   
)

Plots a curve given by implicit equations in 3 variables.

Parameters

sysa list or a list of list of polynomials: the system
v1 = r1v1 is a name of sys and r1 a range of values
v2 = r2v2 is a name of sys and r2 a range of values
v3 = r3v3 is a name of sys and r3 a range of values
grid = i (optional)i is an integer, the number of samples points; default value: 20.
output = keyword (optional)keyword is either list or display: display (resp.  list) returns a graph (resp. a list).

Returns

A graphic: the solutions of the system.

  • when sys is a list of polynomials [p1,...,pk], the graphic is the zeroes of the system p1=0 and ... and pk=0
  • when sys is a list of list of polynomials [L1,...,Lk], the graphic is the union of the zeroes of each system L1, ..., Lk.

Example

> PlotCurve3D ([x^2+y^2-1, z^2-x],grid=100,title="cusp");

Plot3D

Plot3D := proc (
   sys ::{algebraic, equation(algebraic), list({algebraic,equation(algebraic), algebraic<algebraic}), list(list({algebraic,equation(algebraic), algebraic<algebraic}))},  
   ineq ::list({polynom, polynom<polynom}) := [],
   e1 ::name = range := sort ([op(indets([sys,x,y,z],name))])[1] =-5..5,
   e2 ::name = range := sort ([op(indets([sys,x,y,z],name) minus {lhs(e1)})])[1] =-5..5,
   e3 ::name = range := sort ([op(indets([sys,x,y,z],name) minus {lhs(e1),lhs(e2)})])[1] =-5..5,
   {   
   points ::truefalse := false,
   crossingrefine ::truefalse := false,
   grid ::integer := 10,
   border ::constant := 10^(-30),
   output ::identical(list,display) := ':-display'
   }   
)

Plots a system of 3 variables using maple internal plotting functions.

Parameters

sysa list or a list of list of polynomials: the system
v1 = r1v1 is a name of sys and r1 a range of values
v2 = r2v2 is a name of sys and r2 a range of values
v3 = r3v3 is a name of sys and r3 a range of values
points = bool (optional)bool is a boolean: if false, isolated points are ignored; default value: false;
grid = i (optional)i is an integer leading to a grid size i x i; default value: 20.
border = e (optional)e is a numeric value: defines the precision on the border; default value: 0.0001.
crossingrefine = bool (optional)bool is a boolean: if true, the mesh follows the cross of the different surfaces; default value: false.
output = keyword (optional)keyword is either list or display: display (resp.  list) returns a graph (resp. a list).

Returns

A graphic: the solutions of the system.

  • when sys is a polynomial, the graphic is the zeroes of this polynomial
  • when sys is a list of polynomials [p1,...,pk], the graphic is the zeroes of the system p1=0 and ... and pk=0
  • when sys is a list of list of polynomials [L1,...,Lk], the graphic is the union of the zeroes of each system L1, ..., Lk.

Plot3Dglsurf

Plot3Dglsurf := proc (
   sys ::{algebraic, equation(algebraic), list({algebraic,equation(algebraic)}), list(list({algebraic,equation(algebraic)}))},  
   e1 ::name = range,
   e2 ::name = range,
   e3 ::name = range,
   {   
   points ::truefalse := false,
   scale ::identical(constrained, unconstrained) := 'unconstrained'
   }   
)

Plots a system of 3 variables using glsurf.

Parameters

sysa list or a list of list of polynomials: the system
v1 = r1v1 is a name of sys and r1 a range of values
v2 = r2v2 is a name of sys and r2 a range of values
v3 = r3v3 is a name of sys and r3 a range of values
points = bool (optional)bool is a boolean: if false, isolated points are ignored; default value: false;
scaled = keyword (optional)keyword is one of ‘constrained’ or ‘unconstrained’ for the scaling; default value: scaled = unconstrained.

Returns

A graphic: the solutions of the system.

  • when sys is a polynomial, the graphic is the zeroes of this polynomial
  • when sys is a list of polynomials [p1,...,pk], the graphic is the zeroes of the system p1=0 and ... and pk=0
  • when sys is a list of list of polynomials [L1,...,Lk], the graphic is the union of the zeroes of each system L1, ..., Lk.

Plot3Dsurfex

Plot3Dsurfex := proc (
   sys ::{algebraic, equation(algebraic), list({algebraic, equation(algebraic), algebraic<algebraic}), list(list({algebraic,equation(algebraic)}))},  
   ineq ::list({polynom, polynom<polynom}) := [],
   e1 ::name = range := sort ([op(indets([sys,x,y,z]))])[1] =-1..1,
   e2 ::name = range := sort ([op(indets([sys,x,y,z]))])[2] =-1..1,
   e3 ::name = range := sort ([op(indets([sys,x,y,z]))])[3] =-1..1,
   {   
   points ::truefalse := false,
   scale ::identical(constrained, unconstrained) := 'unconstrained'
   }   
)

Plots a system of 3 variables using surfex (software based on surf).

Parameters

sysa list or a list of list of polynomials and/or inequalities: the system
ineq (optional)list of polynomials: extra positive inequalities; default value: []
v1 = r1 (optional)v1 is a name of sys and r1 a range of values; default value: v1=-1..1 where v1 is a variable of sys
v2 = r2 (optional)v2 is a name of sys and r2 a range of values default value: v2=-1..1 where v2 is a variable of sys
v3 = r3 (optional)v3 is a name of sys and r3 a range of values default value: v3=-1..1 where v3 is a variable of sys
points = bool (optional)bool is a boolean: if false, isolated points are ignored; default value: false;
scaled = keyword (optional)keyword is one of ‘constrained’ or ‘unconstrained’ for the scaling; default value: scaled = unconstrained.

Returns

A graphic: the solutions of the system.

  • when sys is a polynomial, the graphic is the zeroes of this polynomial
  • when sys is a list of polynomials [p1,...,pk], the graphic is the zeroes of the system p1=0 and ... and pk=0
  • when sys is a list of list of polynomials [L1,...,Lk], the graphic is the union of the zeroes of each system L1, ..., Lk.

PlotWorkspace

PlotWorkspace := proc (
   robot ::Manipulator,  
   spec ::seq(name=constant),  
   disp ::seq(identical(type1,type2, constraints,infinite)) := ('type1','type2','constraints','infinite'),
   vars ::{list(name), identical(articular, pose)} := 'articular',
   ranges ::seq(name=range) := NULL,
   {   
   notest ::truefalse := false
   }   
      
)

Plot the border of a manipulator workspace

Parameters

robota object of type Manipulator
specsequence of name=constant: the specification of the known variables (the articular values or the pose values, or other)
disp (optional)a sequence of keywords among type1, type2, constraints and infinite: selects the graphics to plot; default value: all the keywords
vars (optional)the display variables, that can be referred as:
  • one of the keyword ‘articular’ or ‘pose’
  • a list of 2 variable names
  • the default value is ‘articular’
  • if ranges is provided, the variables superseed those of vars
ranges (optional)a sequence of the form v1=n1..n2, v2=m1..m2 where v1, v2 are 2 variables and n1,n2,m1,m2 are numerical values; when ranges is not specified, the default range is taken from the field robot:-DefaultPlotRange if it exists, and is -5..5 otherwise.
notest = b (optional)b is a boolean; when b is true the inequality and real constraints are ignored; default value: true;

Returns

A graphic containing:

  • The singularities of type 1
  • The singularities of type 2
  • The configurations with infinitely many solutions in all tha variables (including the passive variables)
  • The border induced by the constraints

Example

> rprrp := Parallel_RPRRP ():
> PlotWorkspace (rprrp, articular);
> PlotWorkspace (rprrp, pose);
> PlotWorkspace (rprrp, [S2,x]);

Configurations

Configurations := proc (robot ::Manipulator,  
spec ::seq(name=constant),  
{   
noconstraints ::truefalse := false,
ordering ::name := NULL
}   )

Computes the different possible positions.

Parameters

robotan object of type Manipulator
specsequence of name=constant: the specification of the known variables (the articular values or the pose values, or other)
noconstraints=*b* (optional)b is a boolean: when true, the constraint inequalities are ignored; default value: false.
ordering (optional)ordering is a name used to order the solutions; default value: NULL

Returns

A list of elements: each elements is a list of name=list(constant) and represents a configuration of the input manipulator.

Example

> rpr := Parallel_3RPR ():
> Configurations (rpr, r1=20, r2=20, r3=20);
[[A1 = [0., 0.], A2 = [15.91, 0.], A3 = [0., 10.00],

    B1 = [1.238874219, -19.96159289], B2 = [18.27856689, -19.85925202],

    B3 = [14.37838350, -3.78571901]], [A1 = [0., 0.], A2 = [15.91, 0.],

    A3 = [0., 10.00], B1 = [-15.37568723, 12.79016193],

    B2 = [1.62170358, 13.99444837], B3 = [-3.30997940, 29.78205101]], [

    A1 = [0., 0.], A2 = [15.91, 0.], A3 = [0., 10.00],

    B1 = [19.99999727, -0.01045036340], B2 = [31.39060352, 12.66297417],

    B3 = [16.87622894, 20.59410427]], [A1 = [0., 0.], A2 = [15.91, 0.],

    A3 = [0., 10.00], B1 = [-13.64842837, -14.61917929],

    B2 = [-4.083315519, -0.51704413], B3 = [-19.53983068, 5.37074264]]]

PlotRobot2D

PlotRobot2D := proc (
   robot ::Manipulator,  
   spec ::seq(name=constant),  
   k ::{integer,range,list(integer)} := ..,
   {   
   color := [],   
   legendvars := subs (map(s->lhs(s)=NULL,[spec]), [op(robot:-ArticularVariables), op(robot:-PoseVariables), op(robot:-PassiveVariables), 'det(J)']),   
   nolegend ::truefalse := false,
   noconstraints ::truefalse := false
   }   
)

Plot a planar manipulator

Parameters

robota Manipulator: the robot to plot
speca sequence of name=constant: specification of variables of the robot to plot
k (optional)an integer: specifies one of the possible configuration when several are available
color=col (optional)equation of the shape color=*col*, where col is a color or a list of colors; when the number of specified color is not enough, deterministic colors are chosen; default value: empty list.
legendvars (optional)list of names: the variables to display in the legend; default value: the articular, passive and pose variables, minus the variables in spec
nolegend=b (optional)b is a boolean: when false, a legend is displayed (the graphic appears in a separate windows with a classic worksheet); default value: false.

Returns

A graphic: the different configurations of the manipulator satisfying the input specifications.  (Maple 13 and higher only)

Example

> rpr := Parallel_3RPR ():
> PlotRobot2D (rpr, r1=20, r2=20, r3=20);
> rr := Parallel_2RR():
> plots:-animate (PlotRobot2D, [rr, theta1=1+t, theta3=2-t], t=0..1);

PlotRobot3D

PlotRobot3D := proc (
   robot ::Manipulator,  
   spec ::seq(name=constant),  
   k ::{integer,range,list(integer)} := ..,
   {   
   color := [],   
   legendvars := subs (map(s->lhs(s)=NULL,[spec]), [op(robot:-ArticularVariables), op(robot:-PoseVariables), op(robot:-PassiveVariables), 'det(J)']),   
   nolegend ::truefalse := false,
   noconstraints ::truefalse := false
   }   
)

Plot a 3D manipulator

Parameters

robota Manipulator: the 3D robot to plot
speca sequence of name=constant: specification of variables of the robot to plot
k (optional)an integer: specifies one of the possible configuration when several are available
color=col (optional)equation of the shape color=*col*, where col is a color or a list of colors; when the number of specified color is not enough, deterministic colors are chosen; default value: empty list.
legendvars (optional)list of names: the variables to display in the legend; default value: the articular, passive and pose variables, minus the variables in spec
nolegend=b (optional)b is a boolean: when false, a legend is displayed (the graphic appears in a separate windows with a classic worksheet); default value: false.

Returns

A graphic: the different configurations of the manipulator satisfying the input specifications.  (Maple 13 and higher only)

Example

> robot := Orthoglide():
> PlotRobot3D (robot, r1=1,r2=1,r3=1, 2);

PlotCell3D

PlotCell3D := proc (cells ::record,  
i ::{list(integer),integer} := [ $ 1 .. nops(cells:-SamplePoints) ],
ranges ::seq(name=range) := NULL,
{   
nowall ::truefalse := false,
grid ::integer := 10,
border ::constant := 0.0000001,
color := []   
}   
   )

Plot the cells returned CellDecomposition or CellDecompositionPlus

Parameters

cellsan object returned by CellDecomposition or CellDecompositionPlus
i (optional)an integer or a list of integer: the indices of the cells to plot in cells. default value: all the cells
ranges (optional)a sequence of the form v=n1..n2 where v is a variable and n1,n2 are numerical values; when not specified for a variable, the default range is -5..5.
grid = i (optional)i is an integer leading to a grid size i x i; default value: 10.
border = e (optional)e is a numeric value: defines the precision on the border; default value: 0.0000001.
nowall = b (optional)b is a boolean; when b is true the vertical faces are not displayed
color = col (optional)equation of the shape color=*col*, where col is a color or a list of colors; when the number of specified color is not enough, deterministic colors are chosen; default value: empty list.  Returns: A 3D plot of the cells indiced by i in cells.

Example

> cells := CellDecompositionPlus ([T],[25-(x^2+y^2+z^2),x+y],[T],[x,y,z]):
> PlotCell3D (cells,[11,15],color=blue);

PlotCell2D

PlotCell2D := proc (
   cells ::record,  
   i ::{list(list(integer)),list(integer),integer} := [ $ 1 .. nops(cells:-SamplePoints) ],
   ranges ::seq(name=range) := NULL,
   {   
   samplepoints ::truefalse := false,
   nowall ::truefalse := false,
   grid ::integer := 10,
   border ::constant := 0.0000001,
   color := [],   
   downupcolors ::list := [],
   points ::list := [],
   colorpoints ::list := []
   }   
      
)

Plot the cells returned CellDecomposition or CellDecompositionPlus

Parameters

cellsan object returned by CellDecomposition or CellDecompositionPlus
i (optional)an integer, a list of integer or a list of list of integer: the indices of the cells to plot in cells. default value: all the cells
ranges (optional)a sequence of the form v=n1..n2 where v is a variable and n1,n2 are numerical values; when not specified for a variable, the default range is -5..5.
grid = i (optional)i is an integer leading to a grid size i x i; default value: 10.
border = e (optional)e is a numeric value: defines the precision on the border; default value: 0.0000001.
nowall = b (optional)b is a boolean: when b is true the vertical faces are not displayed; default value: false.
color = col (optional)equation of the shape color=*col*, where col is a color or a list of colors; when the number of specified color is not enough, deterministic different colors are chosen; default value: empty list.
samplepoints = b (optional)b is a boolean; if true, the labels of the cells are displayed; default value: false.
downupcolors = ducol (optional)list stating the colors of the lower and upper borders of each cell in the follwing form: [[downcol_cell1, upcol_cell1], [downcol_cell2, upcol_cell2],...] default value: empty list.
points = pts (optional)list of coordinates of points to be plot of the form [[x1,y1], [x2,y2], ...] default value: empty list.
colorpoints = colpts (optional)list of colors for the points specified in “points=pts” of the form [col_pt1, col_pt2, ...] default value: empty list.

Returns

A 2D plot of the cells indiced by i in cells.

Example

> cells := CellDecompositionPlus ([T],[25-(x^2+y^2),x+y],[T],[x,y]):
> PlotCell2D (cells,samplepoints);

SetCellColors

SetCellColors := proc (Lc,
Lp)

Set colors to the numbers of solutions obtained by NumberOfSolutionsPlus

Parameters

Lclist returned by NumberOfSolutionsPlus
Lplist returned by DVNumberOfSolutionsPlus

Returns

a list of lists C ready to be used by PlotCell2D: C[1] - contains the numbers of the cells to be plotted C[2] - contains the inner colors for the cells C[3] - contains the colors for the lower and upper borders of the cells C[4] - contains the coordinates of the points to be plotted C[5] - contains the colors for the points to be plotted.

Trajectory

Trajectory := proc (L ::list,  
steps ::integer := 20,
{   
color := []   
}   
   )

Display a given trajectory.

Parameters

Llist or list of list of points in the plane or 3d space.
stepsinteger: the number of interpolated points.
color (optional)a color name or a list of color names; default value: [].

Returns

A plot of the given trajectory:

  • if the input is a list of list of points, then the i-th list is a path colorized with the i-th element of color (or with color directly if it is a color name).  If there is no i-th color, a random color is chosen.
  • if the input is a list of points, then a list of list of points is created by computing steps points between 2 consecutive points.  Then this list of list is displayed.

Example

> Trajectory ( [[0,0],[1,1],[-1,1]],     # the list of vertices
               color=[blue,red] );       # colors of the edges

ImageTrajectory

ImageTrajectory := proc (robot ::Manipulator,  
L ::list,  
pars ::list(name) := robot:-ArticularVariables,
vars ::list(name) := robot:-PoseVariables,
steps ::integer := 20,
{   
color := [],   
loop ::truefalse := false
}   
   )

Display a given trajectory.

Parameters

robotthe manipulator under study
Llist or list of list of points; a point is a list of numerical values, coordinates of the variables pars;
parslist of name; default value: robot[ArticularVariables].
varslist of name: the image space, a list of 2 or 3 variables; default value: robot[PoseVariables].
stepsinteger: the number of interpolated points.
color (optional)a color name or a list of color names; default value: [].
loop (optional)a boolean: if true and L is a list of vertices, then the last point is connected to the first one.

Returns

A plot of the given trajectory:

  • if the input is a list of list of points, then the i-th list is a path colorized with the i-th element of color (or with color directly if it is a color name).  If there is no i-th color, a random color is chosen.
  • if the input is a list of points, then a list of list of points is created by computing steps points between 2 consecutive points.  Then this list of list is displayed.

Example

> robot := ParallelRPR2PRR();
> ImageTrajectory (robot,                       # the manipulator
                   [[0,0,0],[1,1,1],[-1,1,1]],  # the list of vertices
                   [S1,alpha2,alpha3],          # the input variables
                   [phi,x, y],                  # the output variables
                   50,                          # number of inbetween points
                   color=[blue,red],            # colors of the edges
                   symbol=soliddiamond);        # additional plot options
Plot2D := proc (
   sys ::{algebraic, equation(algebraic), list({algebraic,equation(algebraic), algebraic<algebraic}), list(list({algebraic,equation(algebraic), algebraic<algebraic}))},  
   e1 ::name = range,
   e2 ::name = range,
   {   
   points ::truefalse := false,
   [ notest, draft ] ::truefalse := false
   }   
)
Plots a system of 2 variables
PlotCurve3D := proc (
   sys ::{algebraic, equation(algebraic), list({algebraic,equation(algebraic), algebraic<algebraic}), list(list({algebraic,equation(algebraic), algebraic<algebraic}))},  
   ineq ::list({polynom, polynom<polynom}) := [],
   e1 ::name = range := sort ([op(indets([sys,x,y,z],name))])[1] =-5..5,
   e2 ::name = range := sort ([op(indets([sys,x,y,z],name) minus {lhs(e1)})])[1] =-5..5,
   e3 ::name = range := sort ([op(indets([sys,x,y,z],name) minus {lhs(e1),lhs(e2)})])[1] =-5..5,
   {   
   grid ::integer := 30,
   output ::identical(list,display) := ':-display'
   }   
)
Plots a curve given by implicit equations in 3 variables.
Plot3D := proc (
   sys ::{algebraic, equation(algebraic), list({algebraic,equation(algebraic), algebraic<algebraic}), list(list({algebraic,equation(algebraic), algebraic<algebraic}))},  
   ineq ::list({polynom, polynom<polynom}) := [],
   e1 ::name = range := sort ([op(indets([sys,x,y,z],name))])[1] =-5..5,
   e2 ::name = range := sort ([op(indets([sys,x,y,z],name) minus {lhs(e1)})])[1] =-5..5,
   e3 ::name = range := sort ([op(indets([sys,x,y,z],name) minus {lhs(e1),lhs(e2)})])[1] =-5..5,
   {   
   points ::truefalse := false,
   crossingrefine ::truefalse := false,
   grid ::integer := 10,
   border ::constant := 10^(-30),
   output ::identical(list,display) := ':-display'
   }   
)
Plots a system of 3 variables using maple internal plotting functions.
Plot3Dglsurf := proc (
   sys ::{algebraic, equation(algebraic), list({algebraic,equation(algebraic)}), list(list({algebraic,equation(algebraic)}))},  
   e1 ::name = range,
   e2 ::name = range,
   e3 ::name = range,
   {   
   points ::truefalse := false,
   scale ::identical(constrained, unconstrained) := 'unconstrained'
   }   
)
Plots a system of 3 variables using glsurf.
Plot3Dsurfex := proc (
   sys ::{algebraic, equation(algebraic), list({algebraic, equation(algebraic), algebraic<algebraic}), list(list({algebraic,equation(algebraic)}))},  
   ineq ::list({polynom, polynom<polynom}) := [],
   e1 ::name = range := sort ([op(indets([sys,x,y,z]))])[1] =-1..1,
   e2 ::name = range := sort ([op(indets([sys,x,y,z]))])[2] =-1..1,
   e3 ::name = range := sort ([op(indets([sys,x,y,z]))])[3] =-1..1,
   {   
   points ::truefalse := false,
   scale ::identical(constrained, unconstrained) := 'unconstrained'
   }   
)
Plots a system of 3 variables using surfex (software based on surf).
PlotWorkspace := proc (
   robot ::Manipulator,  
   spec ::seq(name=constant),  
   disp ::seq(identical(type1,type2, constraints,infinite)) := ('type1','type2','constraints','infinite'),
   vars ::{list(name), identical(articular, pose)} := 'articular',
   ranges ::seq(name=range) := NULL,
   {   
   notest ::truefalse := false
   }   
      
)
Plot the border of a manipulator workspace
Configurations := proc (robot ::Manipulator,  
spec ::seq(name=constant),  
{   
noconstraints ::truefalse := false,
ordering ::name := NULL
}   )
Computes the different possible positions.
PlotRobot2D := proc (
   robot ::Manipulator,  
   spec ::seq(name=constant),  
   k ::{integer,range,list(integer)} := ..,
   {   
   color := [],   
   legendvars := subs (map(s->lhs(s)=NULL,[spec]), [op(robot:-ArticularVariables), op(robot:-PoseVariables), op(robot:-PassiveVariables), 'det(J)']),   
   nolegend ::truefalse := false,
   noconstraints ::truefalse := false
   }   
)
Plot a planar manipulator
PlotRobot3D := proc (
   robot ::Manipulator,  
   spec ::seq(name=constant),  
   k ::{integer,range,list(integer)} := ..,
   {   
   color := [],   
   legendvars := subs (map(s->lhs(s)=NULL,[spec]), [op(robot:-ArticularVariables), op(robot:-PoseVariables), op(robot:-PassiveVariables), 'det(J)']),   
   nolegend ::truefalse := false,
   noconstraints ::truefalse := false
   }   
)
Plot a 3D manipulator
PlotCell3D := proc (cells ::record,  
i ::{list(integer),integer} := [ $ 1 .. nops(cells:-SamplePoints) ],
ranges ::seq(name=range) := NULL,
{   
nowall ::truefalse := false,
grid ::integer := 10,
border ::constant := 0.0000001,
color := []   
}   
   )
Plot the cells returned CellDecomposition or CellDecompositionPlus
PlotCell2D := proc (
   cells ::record,  
   i ::{list(list(integer)),list(integer),integer} := [ $ 1 .. nops(cells:-SamplePoints) ],
   ranges ::seq(name=range) := NULL,
   {   
   samplepoints ::truefalse := false,
   nowall ::truefalse := false,
   grid ::integer := 10,
   border ::constant := 0.0000001,
   color := [],   
   downupcolors ::list := [],
   points ::list := [],
   colorpoints ::list := []
   }   
      
)
Plot the cells returned CellDecomposition or CellDecompositionPlus
SetCellColors := proc (Lc,
Lp)
Set colors to the numbers of solutions obtained by NumberOfSolutionsPlus
Trajectory := proc (L ::list,  
steps ::integer := 20,
{   
color := []   
}   
   )
Display a given trajectory.
ImageTrajectory := proc (robot ::Manipulator,  
L ::list,  
pars ::list(name) := robot:-ArticularVariables,
vars ::list(name) := robot:-PoseVariables,
steps ::integer := 20,
{   
color := [],   
loop ::truefalse := false
}   
   )
Display a given trajectory.
Close