Modelica.Mechanics.MultiBody.Visualizers.Advanced.SurfaceCharacteristics

Information

This package contains functions that are used to define parameterized surfaces for use with the Surface model.

Extends from Modelica.Icons.Package (Icon for standard packages).

Package Content

Name	Description
torus	Function defining the surface characteristic of a torus
pipeWithScalarField	Function defining the surface characteristic of a pipe where a scalar field value is displayed with color along the pipe axis

Modelica.Mechanics.MultiBody.Visualizers.Advanced.SurfaceCharacteristics.torus

Information

Function torus computes the X,Y,Z arrays to visualize a torus with model Torus. The left image below shows a torus with ri=0.5 m and ro = 0.2 m. The right images below shows the torus with the additional parameter settings:

  opening    =   45 degree
  startAngle = -135 degree
  stopAngle  =  135 degree

Extends from Modelica.Mechanics.MultiBody.Interfaces.partialSurfaceCharacteristic.

Inputs

Type	Name	Default	Description
Integer	nu		Number of points in u-Dimension
Integer	nv		Number of points in v-Dimension
Boolean	multiColoredSurface	false	= true: Color is defined for each surface point
Radius	ri	1	Inner radius of torus [m]
Radius	ro	0.2	Outer radius of torus (=width/2) [m]
Angle	opening	0	Opening angle of torus [rad]
Angle	startAngle	-Modelica.Constants.pi	Start angle of torus slice [rad]
Angle	stopAngle	Modelica.Constants.pi	End angle of torus slice [rad]

Outputs

Type	Name	Description
Position	X[nu, nv]	[nu,nv] positions of points in x-Direction resolved in surface frame [m]
Position	Y[nu, nv]	[nu,nv] positions of points in y-Direction resolved in surface frame [m]
Position	Z[nu, nv]	[nu,nv] positions of points in z-Direction resolved in surface frame [m]
Real	C[if multiColoredSurface then nu else 0, if multiColoredSurface then nv else 0, 3]	[nu,nv,3] Color array, defining the color for each surface point

Modelica definition

function torus 
  "Function defining the surface characteristic of a torus"
  extends Modelica.Mechanics.MultiBody.Interfaces.partialSurfaceCharacteristic(
            final multiColoredSurface=false);
  input Modelica.SIunits.Radius ri=1 "Inner radius of torus";
  input Modelica.SIunits.Radius ro=0.2 "Outer radius of torus (=width/2)";
  input Modelica.SIunits.Angle opening=0 "Opening angle of torus";
  input Modelica.SIunits.Angle startAngle= -Modelica.Constants.pi 
    "Start angle of torus slice";
  input Modelica.SIunits.Angle stopAngle= Modelica.Constants.pi 
    "End angle of torus slice";
protected 
  Modelica.SIunits.Angle alpha;
  Modelica.SIunits.Angle beta;
  Modelica.SIunits.Angle phi_start;
  Modelica.SIunits.Angle phi_stop;
algorithm 
  phi_start :=-Modelica.Constants.pi + opening;
  phi_stop  :=Modelica.Constants.pi - opening;
  for i in 1:nu loop
      alpha := startAngle + (stopAngle-startAngle)*(i-1)/(nu-1);
      for j in 1:nv loop
          beta := phi_start + (phi_stop-phi_start)*(j-1)/(nv-1);
          X[i,j] := (ri + ro*cos(beta))*sin(alpha);
          Y[i,j] := ro*sin(beta);
          Z[i,j] := (ri + ro*cos(beta))*cos(alpha);
      end for;
  end for;
end torus;

Modelica.Mechanics.MultiBody.Visualizers.Advanced.SurfaceCharacteristics.pipeWithScalarField

Information

Function pipeWithScalarField computes the X,Y,Z,C arrays in order to visualize a pipe and a scalar field along the pipe axis with model PipeWithScalarField. The latter is shown by mapping scalar field to color values with a color map and utilizing this color at the perimeter associated with the corresponding axis location. Typically the scalar field value is a temperature, but might be also another quantity. Predefined color maps are available from MultiBody.Visualizers.Colors.ColorMaps and can be selected via input argument "colorMap". A color map with the corresponding scalar field values can be exported as vector-graphics in svg-format with function MultiBody.Visualizers.Colors.colorMapToSvg. An example is shown in the next figure:

The color coding is shown in the next figure. It was generated with Mechanics.MultiBody.Visualizers.Colors.colorMapToSvg using the following call:

colorMapToSvg(Modelica.Mechanics.MultiBody.Visualizer.Colors.ColorMap.jet(),
              height=50, nScalars=6, T_max=100, heading="Temperature in C");

Extends from Modelica.Mechanics.MultiBody.Interfaces.partialSurfaceCharacteristic.

Inputs

Type	Name	Default	Description
Integer	nu		Number of points in u-Dimension
Integer	nv		Number of points in v-Dimension
Boolean	multiColoredSurface	true	= true: Color is defined for each surface point
Radius	rOuter		Outer radius of cylinder [m]
Length	length		Length of cylinder [m]
Position	xsi[:]		Relative position along the pipe with x[1] = 0, x[end] = 1 [m]
Real	T[size(xsi, 1)]		Scalar field value at position xsi*length
Real	T_min		T <= T_min is mapped to colorMap[1,:]
Real	T_max		T >= T_max is mapped to colorMap[end,:]
Real	colorMap[:, 3]		Color map to map scalar T to a corresponding color

Outputs

Type	Name	Description
Position	X[nu, nv]	[nu,nv] positions of points in x-Direction resolved in surface frame [m]
Position	Y[nu, nv]	[nu,nv] positions of points in y-Direction resolved in surface frame [m]
Position	Z[nu, nv]	[nu,nv] positions of points in z-Direction resolved in surface frame [m]
Real	C[if multiColoredSurface then nu else 0, if multiColoredSurface then nv else 0, 3]	[nu,nv,3] Color array, defining the color for each surface point

Modelica definition

function pipeWithScalarField 
  "Function defining the surface characteristic of a pipe where a scalar field value is displayed with color along the pipe axis"
  import C = Modelica.Constants;
  extends Modelica.Mechanics.MultiBody.Interfaces.partialSurfaceCharacteristic(
            final multiColoredSurface=true);
  input Modelica.SIunits.Radius rOuter "Outer radius of cylinder";
  input Modelica.SIunits.Length length "Length of cylinder";
  input Modelica.SIunits.Position xsi[:] 
    "Relative position along the pipe with x[1] = 0, x[end] = 1";
  input Real T[size(xsi,1)] "Scalar field value at position xsi*length";
  input Real T_min "T <= T_min is mapped to colorMap[1,:]";
  input Real T_max "T >= T_max is mapped to colorMap[end,:]";
  input Real colorMap[:,3] "Color map to map scalar T to a corresponding color";
protected 
  Real beta;
  Real xsi_i;
  Real Ti;
  Real Ci[3];
  Integer k;
algorithm 
  k:=1;
  for i in 1:nu loop
     // Compute actual xsi-position along cylinder axis
     xsi_i := (i-1)/(nu-1);

     // Interpolate in xsi and T to determine the corresponding value of Ti(xsi_i)
     (Ti,k) := Modelica.Math.Vectors.interpolate(xsi, T, xsi_i, k);

     // Map the scalar field value Ti to a color value
     Ci := Modelica.Mechanics.MultiBody.Visualizers.Colors.scalarToColor(
                                              Ti, T_min, T_max, colorMap);

     // Determine outputs
     for j in 1:nv loop
        beta := 2*Modelica.Constants.pi*(j-1)/(nv-1);
        X[i,j] := length*xsi_i;
        Y[i,j] := rOuter*sin(beta);
        Z[i,j] := rOuter*cos(beta);
        C[i,j,:] := Ci;
     end for;
  end for;
end pipeWithScalarField;