Mathematical Form Scripts
RhinoCommon Code
Mobius
Implemented in a VB.NET scripting component for Grasshopper.
Private Sub RunScript(ByVal U As Integer, ByVal V As Integer, ByVal R As Double, ByVal T As Double, ByVal S As Double, ByVal D1 As Interval, ByVal D2 As Interval, ByRef Srf As Object)
Dim pointslist As New List (Of Point3d)
Dim psurface As NurbsSurface
Dim urange0 As Double = D1.Min
Dim urange1 As Double = D1.Max
Dim vrange0 As Double = D2.Min
Dim vrange1 As Double = D2.Max
Dim ustep As Double = Math.Abs(urange1 - urange0) / (U - 1)
Dim vstep As Double = Math.Abs(vrange1 - vrange0) / (V - 1)
Dim ucount As Double = 0
Dim vcount As Double = 0
For i As Double = urange0 To urange1 Step ustep
vcount = 0
For j As Double = vrange0 To vrange1 Step vstep
Dim x As Double = (R + j * Math.cos(T * i)) * Math.cos(i)
Dim y As Double = (R + j * Math.cos(T * i)) * Math.sin(i)
Dim z As Double = j * Math.sin(T * i)
Dim mypoint As New Point3d(x * S, y * S, z * S)
pointslist.Add(mypoint)
vcount = vcount + 1
Next
ucount = ucount + 1
Next
psurface = NurbsSurface.CreateFromPoints(pointslist, ucount, vcount, 2, 2)
Srf = psurface
End Sub
Klein
Implemented in a VB.NET scripting component for Grasshopper.
Private Sub RunScript(ByVal U As Integer, ByVal V As Integer, ByVal R As Double, ByVal T As Double, ByVal S As Double, ByVal D1 As Interval, ByVal D2 As Interval, ByRef Srf As Object)
Dim pointslist As New List (Of Point3d)
Dim psurface As NurbsSurface
Dim urange0 As Double = D1.Min
Dim urange1 As Double = D1.Max
Dim vrange0 As Double = D2.Min
Dim vrange1 As Double = D2.Max
Dim ustep As Double = Math.Abs(urange1 - urange0) / (U - 1)
Dim vstep As Double = Math.Abs(vrange1 - vrange0) / (V - 1)
Dim ucount As Double = 0
Dim vcount As Double = 0
For i As Double = urange0 To urange1 Step ustep
vcount = 0
For j As Double = vrange0 To vrange1 Step vstep
Dim x As Double = (R + Math.cos(T * i) * Math.sin(j) - Math.sin(T * i) * Math.sin(2 * j)) * Math.cos(i)
Dim y As Double = (R + Math.cos(T * i) * Math.sin(j) - Math.sin(T * i) * Math.sin(2 * j)) * Math.sin(i)
Dim z As Double = Math.sin(T * i) * Math.sin(j) + Math.cos(T * i) * Math.sin(2 * j)
Dim mypoint As New Point3d(x * S, y * S, z * S)
pointslist.Add(mypoint)
vcount = vcount + 1
Next
ucount = ucount + 1
Next
psurface = NurbsSurface.CreateFromPoints(pointslist, ucount, vcount, 2, 2)
Srf = psurface
End Sub
Processing
Supershape 3D
Implemented using the iGeo library.
import igeo.*; import processing.opengl.*; size(480, 360, IG.GL); //supershape parameters float m = 14.23; float a = -0.06; float b = 2.78; float n1 = 3.74; float n2 = -.48; float n3 = 1.46; int unum = 50; int vnum = 50; float uinc = PI/(unum/2); float vinc = (PI/2)/(vnum/2); //points array IVec[][] mypts = new IVec[unum+1][vnum+1]; //math stuff float theta = -PI; for(int i = 0; i<=unum; i++) { float phi = -PI/2; float r1 = 1/pow(pow(abs(cos(m*theta/4)/a),n2) + pow(abs(sin(m*theta/4)/b), n3), 1/n1); for(int j = 0; j<=vnum; j++){ float r2 = 1/pow(pow(abs(cos(m*phi/4)/a),n2) + pow(abs(sin(m*phi/4)/b),n3), 1/n1); float x = r1*cos(theta) * r2*cos(phi); float y = r1*sin(theta) * r2*cos(phi); float z = r2*sin(phi); mypts[i][j] = new IVec(x,y,z); new IPoint(x,y,z).clr(abs(1./theta),0,abs(1./phi)); phi = phi + vinc; } theta = theta + uinc; } //create new surface new ISurface(mypts);
Revit API
Sine Surface
Implemented within the Revit API as a conceptual mass.
Dim ref_ar_ar As ReferenceArrayArray = New ReferenceArrayArray()
Dim XYZ As Autodesk.Revit.Geometry.XYZ
For u As Double = 0 To 4 * Math.PI Step Math.PI / 4
Dim rfptsarr As ReferencePointArray = New ReferencePointArray()
For v As Double = 0 To 4 * Math.PI Step Math.PI / 4
Dim refpt As Autodesk.Revit.Elements.ReferencePoint
Dim x As Double
Dim y As Double
Dim z As Double
x = 10 * u
y = 10 * v
z = 10 * Math.Cos(u) + 10 * Math.Sin(v)
XYZ = revit_app.Create.NewXYZ(x, y, z)
refpt = revit_doc.FamilyCreate.NewReferencePoint(XYZ)
rfptsarr.Append(refpt)
Next
Dim crv As CurveByPoints = revit_doc.FamilyCreate.NewCurveByPoints(rfptsarr)
Dim ref_ar As ReferenceArray = New ReferenceArray()
ref_ar.Append(crv.GeometryCurve.Reference)
ref_ar_ar.Append(ref_ar)
Next
Dim loftform As Autodesk.Revit.Elements.Form = revit_doc.FamilyCreate.NewLoftForm(True, ref_ar_ar)
Supershape3D using RevitPythonShell
Implemented using RevitPythonShell in a conceptual mass.
import math import clr clr.AddReference('RevitAPI') clr.AddReference('RevitAPIUI') from Autodesk.Revit.DB import * doc = __revit__.ActiveUIDocument.Document t = Transaction(doc,'undo') t.Start() #This script creates a 3D Supershape using lofted segments. #Copyright (c) 2011, Nathan Miller, The Proving Ground #The Proving Ground, http://nmillerarch.blogspot.com #3D supershape parameters m = 15.97 a = 0.0486 b = 5.36 n1 = .2624 n2 = -.29 n3 = 1.5 ustep = 50 vstep = 50 piA = math.pi *.5 piB = math.pi *.5 #Because curves will eventually become absorbed into the loft form, it is important to create two sets of the same curve. #This method is a workaround for being unable to connect all curves into one single lofted shape. #Create ReferenceArrayArrays refarar1 = ReferenceArrayArray() refarar2 = ReferenceArrayArray() #The math part... theta = -piA while (theta <= piA): phi = -piB/2 r1 = 1/(((abs(math.cos(m*theta/4)/a))**n2+(abs(math.sin(m*theta/4)/b))**n3)**n1) refptsarr = ReferencePointArray() while (phi <= piB/2): r2 = 1/(((abs(math.cos(m*phi/4)/a))**n2+(abs(math.sin(m*phi/4)/b))**n3)**n1) x = r1 * math.cos(theta) * r2 * math.cos(phi) y = r1 * math.sin(theta) * r2 * math.cos(phi) z = r2 * math.sin(phi) myXYZ = XYZ(x,y,z) refptsarr.Append(doc.FamilyCreate.NewReferencePoint(myXYZ)) #Increment phi phi = phi + (piB/2 / (vstep/2)) #Increment theta theta = theta + (piA / (ustep/2)) #Comment out everything below to quickly test the point cloud shapes #Surface geometry takes a long time to generate.... needs to be faster! #create the curves crv1 = doc.FamilyCreate.NewCurveByPoints(refptsarr) crv2 = doc.FamilyCreate.NewCurveByPoints(refptsarr) #create reference arrays refar1 = ReferenceArray() refar2 = ReferenceArray() #Append curve refences to the reference arrays refar1.Append(crv1.GeometryCurve.Reference) refar2.Append(crv2.GeometryCurve.Reference) #Append ReferenceArrays to ReferenceArrayArrays refarar1.Append(refar1) refarar2.Append(refar2) #Get the number of curves stored in the ReferenceArAr. refsize = refarar1.Size #Loft pairs of curves together for a segmented surface. for i in range(0,refsize-1): loftar = ReferenceArrayArray() loftar.Append(refarar1[i]) loftar.Append(refarar2[i+1]) doc.FamilyCreate.NewLoftForm(True, loftar) t.Commit() __window__.Close()
License
The code and components on this page are free software: you can redistribute them and/or modify them under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.