Surfaces of translation

Surfaces of translation#

See also: https://en.wikipedia.org/wiki/Translation_surface_(differential_geometry)

See also:http://www.3d-meier.de/tut3/Seite0.html

See also: https://en.wikipedia.org/wiki/Implicit_surface

Fermat spiral as generator#

The XML code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D01a_FermatSpiral.3D.xml (D01a-c).

The example below uses the following code in C#

var h = 2;
var x = 4*Math.Sqrt(u) * Math.Cos(u);
var y = 4*Math.Sqrt(u) * Math.Sin(u);
var z = h * v;

See also Wikipedia [1368], MathWorld [1070].

D01a_FermatSpiral.3D \(\quad\) D01b_FermatSpiral.3D \(\quad\) D01c_FermatSpiral.3D

Lemniscate as generator#

The XML code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the files D02a_Lemniscate.3D.xml (D02a-c).

The example below uses the following code in C#

double a = 0.3;
double c = 1.0;
double r = c * 0.5;
var x = r * (Math.Cos(u) / (1 + Math.Sin(u) * Math.Sin(u)));
var y = r * (Math.Sin(u) * Math.Cos(u) / (1 + Math.Sin(u) * Math.Sin(u)));
var z = a * v;

// see also: http://www.3d-meier.de/tut3/Seite152.html

See also Wikipedia [1368], MathWorld [1070].

D02a_Lemniscate.3D \(\quad\) D02b_Lemniscate.3D \(\quad\) D02c_Lemniscate.3D

Tanh spiral as generator#

The XML code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the files D03a_TanhSpiral.3D.xml (D03a-c).

The example below uses the following code in C#

var h = 0.5;
double c = 0.2;
double a = 6.0;
var x = c * (Math.Sinh(2 * u) / (Math.Cos(2 * a * u) + Math.Cosh(2 * u)));
var y = c * (Math.Sin(2 * a * u) / (Math.Cos(2 * a * u) + Math.Cosh(2 * u)));
var z = h * v;

// see http://www.3d-meier.de/tut3/Seite187.html // see Krivoshapko, p. 498

See also Wikipedia [1368], MathWorld [1070].

See also Wikipedia [1368], MathWorld [1070].

D03a_TanhSpiral.3D \(\quad\) D03b_TanhSpiral.3D \(\quad\) D03c_TanhSpiral.3D

Rose curve as generator#

The XML code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the files D04a_RoseCurve.3D.xml (D04a-c).

The example below uses the following code in C#

double a = 0.6;
double h = 2.0;
double n = 3.0;
double ca = Math.Cos(a);

var x = (h * Math.Abs(Math.Cos(n * u)) * ca) * Math.Cos(u);
var y = (h * Math.Abs(Math.Cos(n * u)) * ca) * Math.Sin(u);
var z = a * v;

// see http://www.3d-meier.de/tut3/Seite189.html

See also Wikipedia [1368], MathWorld [1070].

D04a_RoseCurve.3D \(\quad\) D04b_RoseCurve.3D \(\quad\) D04c_RoseCurve.3D

Hypocycloid as generator#

The XML code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the files D05a_Hypocycloid_55.3D.xml (D05a-c).

The example below uses the following code in C#

double a = 3.7;
double r = 1.5;
double k = 5.5;
var x = r * (k - 1) * Math.Cos(u) + r * Math.Cos((k - 1) * u);
var y = r * (k - 1) * Math.Sin(u) - r * Math.Sin((k - 1) * u);
var z = a * v;

// see http://www.3d-meier.de/tut3/Seite189.html

See also Wikipedia [1368], MathWorld [1070].

D05a_Hypocycloid_55.3D \(\quad\) D05b_Hypocycloid_55.3D \(\quad\) D05c_Hypocycloid_55.3D

Epicycloid as generator#

The XML code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the files D06a_Epicycloid_55.3D.xml (D06a-c).

The example below uses the following code in C#

double a = 2.0;
double r = 1.0;
double k = 5.5;
var h = 1.5;
var x = r * (k + 1) * Math.Cos(u) - h * r * Math.Cos((k + 1) * u);
var y = r * (k + 1) * Math.Sin(u) - h * r * Math.Sin((k + 1) * u);
var z = a * v;

// see http://www.3d-meier.de/tut3/Seite189.html

See also Wikipedia [1368], MathWorld [1070].

D06a_Epicycloid_55.3D \(\quad\) D06b_Epicycloid_55.3D \(\quad\) D06c_Epicycloid_55.3D

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