Page 300 - DMTH402_COMPLEX_ANALYSIS_AND_DIFFERENTIAL_GEOMETRY

Unit 23: Developable Surface Fitting to Point Clouds

4. Let the plane P = H  H be given by equations. The pencil of three spaces H + H 2 Notes
1
2
1
contains a unique three-space H, passing through the origin in  , whose equation is
4
................
5. D is a smooth surface not carrying singular points. D is not necessarily exactly developable,
but one can run the ................ also for nearly developable surfaces (one small principal
curvature).
6. Computation of the boundary curves of D* with respect to the domain of interest in
................

23.9 Review Questions

1. Discuss The Blaschke Model of Oriented Planes in R .
3
2. Explain Incidence of Point and Plane.
3. Define Tangency of Sphere and Plane.
4. Discuss the Classification of Developable Surfaces according to their Image on B.
5. Describe Cones and Cylinders of Revolution.

6. Explain Recognition of Developable Surfaces from Point Clouds.
7. Describe Reconstruction of Developable Surfaces from Measurements.

Answers: Self Assessment

1. S : (x – m) – r 2 2. developable
2
3
3. tangent planes 4. H :  u (sp – rq ) + u (s – r) = 0.
i
i
4
i
i=1
5. algorithm 6.  .
3
23.10 Further Readings

Books Ahelfors, D.V. : Complex Analysis
Conway, J.B. : Function of one complex variable
Pati, T. : Functions of complex variable
Shanti Narain : Theory of function of a complex Variable
Tichmarsh, E.C. : The theory of functions
H.S. Kasana : Complex Variables theory and applications
P.K. Banerji : Complex Analysis
Serge Lang : Complex Analysis
H. Lass : Vector & Tensor Analysis
Shanti Narayan : Tensor Analysis
C.E. Weatherburn : Differential Geometry
T.J. Wilemore : Introduction to Differential Geometry
Bansi Lal : Differential Geometry.

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