| Week 7 | |
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| Course | Arch 2042 |
| Date | 2012/04/13 |
| Learning Objectives | We continue our treatment of surfaces, showing how other coordinate geometries can often simplify a parametric description to one that includes a rectangular domain. We will also show a number of examples of surfaces including graphs, planes and other non-graph surfaces. The in-class exercise will involve modeling and panelizing surfaces, which will illustrate how different ways of modeling determines different parametrizations and therefore different panelizations given by the isocurves. |
| Agenda |
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| Uses Tool(s) | |
Surfaces
This is the material that we covered in class on parametrizing surfaces .
As you work through the examples, it will be useful for you to visualize some of the examples (as well as your own creations) using this piece of code DrawParametricSurface.py which currently only takes a rectangular domain.
import rhinoscriptsyntax as rs import math def DrawParametricSurface(parametric_equation): "Draw points on a surface based on a parametric equation." # Currently only for a rectangular domain - get the minimum and maximum parameters for this domain u0 = rs.GetReal("Minimum u value", 0.0) if( u0==None ): return u1 = rs.GetReal("Maximum u value", 1.0) if( u1==None ): return v0 = rs.GetReal("Minimum v value", 0.0) if( v0==None ): return # Get the maximum parameter v1 = rs.GetReal("Maximum v value", 1.0) if( v1==None ): return # Get the number of sampling points to interpolate through count = rs.GetInteger("Number of points in both u and v directions", 50, 2) #pSurface = [] #Get the rest of the points step_u = (u1-u0)/count step_v = (v1-v0)/count for i in range(count): u = u0 + i*step_u for j in range(count): v = v0 + j*step_v point = parametric_equation(u,v) rs.AddPoint(point) #pSurface.append(point) #Customizable function that solves a parametric equation def __CalculatePoint(u,v): #ex 1a. any graph z = f(x,y); doman = [-10, 10] x [-10, 10] #x = u #y = v #z = math.sqrt(u**2 + v**2) #z = math.cos(math.sqrt(u**2+v**2)) # ex 1b. a cone parametrized in cylindrical coordinates; domain = [0, 2*pi]x[0, 5] #x = v*math.cos(u) #y = v*math.sin(u) #z = v #ex 2. Helicoid; domain = [0, 2*pi]x[r1,r2] #x = v*math.cos(u) #y = v*math.sin(u) #z = u #ex 3. Catenoid; domain = [0, 2*pi]x[a,b] #x = 5*math.cosh(v/5)*math.cos(u) #y = 5*math.cosh(v/5)*math.sin(u) #z = v #ex 4. Hyperboloid: #x = 2*math.sqrt(1 + v**2)*math.cos(u) #y = 2*math.sqrt(1 + v**2)*math.sin(u) #z = v #ex 5. Elliptic Hyperboloid #x = 2*math.sqrt(1 + v**2)*math.cos(u) #y = 5*math.sqrt(1 + v**2)*math.sin(u) #z = 10*v #ex 6. Torus; domain = [0, 2*pi]x[-3,3] x = (2-math.cos(v))*math.cos(u) y = (2-math.cos(v))*math.sin(u) z = math.sin(v) return x,y,z ########################################################################## # Check to see if this file is being executed as the "main" python # script instead of being used as a module by some other python script # This allows us to use the module which ever way we want. if( __name__ == "__main__" ): #Call the function passing another function as a parameter DrawParametricSurface(__CalculatePoint)
In-class assignment: Panelizing Surfaces
Assignment
Prepare a 1-page final project brief. This should include a problem statement, relevant context (images of site, building details), anticipated process. Please have this in your dropbox before class on April 20 .