thorough understanding of subdivision surfaces

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FOR Essay 1
OBJECTIVES
The main objectives of this active learning project are (1) to gain a thorough understanding of subdivision surfaces, (2) to survey the literature to find existing techniques and (3) to report on a particular technique appropriate in a NURBS modeling environment used for animation.
PROJECT DESCRIPTION
This project consists of the following simple elements:
Understand the concept of subdivision surfaces as used in the modeling practice.
Perform a search on topics like “subdivision surfaces”, “refinement method”, “mesh based design”, “unrestricted topology”, etc.
Do a search on “subdivision surfaces” and dig out all useful and understandable information.
Find publicly available code and/or demo programs related to subdivision surface design.
Once the research is done, digest all the information you gathered and write-up your experience with your independent research as described in the next section.
DELIVERABLES
Using this file as a template write an essay of about 5,000 words that contains, as a minimum, the following components:
A short abstract of no more than 200 words.
A list of keywords of no more than 5.
An introduction section where you describe the problem domain and give a short description of prior approaches as far as you know.
A section on mesh-based methods.
A section on subdivision surfaces, which describes the result of your independent research.
A section on algorithm design where you show a code architecture and/or flow chart to subdivision surface based design.
Proper illustrations throughout the text.
A section on examples and demos, if any.
A section on experiments, if available or if you have done one or more yourself.
Should be of minimum of 7 pages
 For Essay 2
Ray casting nurbs surface (7 pages)
OBJECTIVES
The main objectives of this active learning project are (1) to gain a thorough understanding of ray-casting methods as applied to line-NURBS intersection, (2) to study the literature on published methods and (3) to report on a viable technique that solves the problem with reasonable efficiency.
PROJECT DESCRIPTION
This project consists of the following simple elements:
Understand the concept of ray-casting as applied in NURBS surface visualization using ray tracing.
Perform a search on topics like “ray tracing NURBS”, “line-surface intersection”, “ray- casting”, etc, and find all useful and relevant information to be able to design a ray-caster.
Find publicly available code and/or demo programs related to ray tracing, NURBS and visualization with NURBS.
Once the research is done, digest all the information you gathered and write-up your experience with your independent research as described in the next section.
DELIVERABLES
Using this file as a template, write an essay of about 5,000 words that contains, as a minimum, the following components:
A short abstract of no more than 200 words.
A list of keywords of no more than 5.
An introduction section where you describe the problem domain and give a short description of prior approaches as far as you know.
A section on general ray-casting methods.
A section on ray-casting NURBS curves and surfaces, which describes the result of your independent research.
A section on algorithm design where you show a code architecture and/or flow chart to ray trace NURBS entities.
Proper illustrations throughout the text.
A section on examples and demos, if any.
A section on experiments, if available or if you have done one or more yourself.

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