Lecture 12 - Spline surfaces (slides)

Lecture 12 spline surfaces slides

Info icon This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Interactive Computer Graphics: 
 Lecture 12 " Introduction to Surface Construction ! Teapot Subdivision: Russ Fish Teapot Subdivision: Russ Fish " Graphics Lecture 12: Slide 2! 2 / 35 Non Parametric Surface" •  Surfaces can be constructed from Cartesian equations directly, and this is acceptable for specific applications, usually involving interpolation. ! •  As before, using a simple polynomial surface is a quick and easy approach. ! Graphics Lecture 12: Slide 3! Non Parametric Polynomial Surface Non on Parametric Polynomial Surface " N Parametric Polynomial Surface 00 11 011 0 a a b b c c d d xx BB e f g CC BCC b b e f C By C g C By C 0 B x x y y z z 1 1BB @@ f h j AA @AA = 0 @z = cc f h j z ddgg j j 11 11 whichwhich multiplies out to: ! •  multiplies out to: which multiplies out to: 2 ey 2 2 hz 2 2 2 ax2 ++ ey++ hz++bxy ++cxz ++f yz ++dx ++gy ++jz ++ 1 = 0 ax 2bxy 2 2cxz 2 2f yz 2 2dx 2 2gy 2 2jz 1 = 0 Because ofof theof the symmetryare 9 scalar 9 scalar inin the •  Because symmetry there 9 scalar unknowns the Because the symmetry there arethere are unknownsunknowns in equation equation ! the equation •  So we need to specify nine points through which the So we need toto specify nine points through which the surface will So we need will pass ! points through which the surface will surface specify nine pass pass Graphics Lecture 12: Slide 4! As Before " •  This formulation suffers the same problems as the nonparametric spline curve. It is a fixed surface for a given set of nine points. ! •  We need more flexibility for the design of surfaces. ! Graphics Lecture 12: Slide 5! Simple Parametric surfaces Simple Parametric surfaces Simple Parametric surfaces " We can extend the formulation to simple parametric surfaces using •  can extend the equation: WeWe can extendformulation to simplesimple parametric using the vector the formulation to parametric surfaces urfaces using ! thesvector equation:the vector equation: 0 10 1 abc µ 0 10 1 a 1) c µ P(µ, ⌫ ) = (µ, ⌫, b @b d eA @⌫ A P(µ, ⌫ ) = (µ, ⌫, 1) @b d eA @⌫ A cef 1 cef 1 2 2 P(µ, ⌫ ) = aµ + d⌫ + 2bµ⌫ + 2cµ + 2...
View Full Document

  • Spring '14
  • Surface, Parametric equation, Parametric surface

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern