 # Презентация на тему: Topic 3                             1/29
Средняя оценка: 4.8/5 (всего оценок: 63)
Код скопирован в буфер обмена
1

## Первый слайд презентации: Topic 3

3D Objects General curves & surfaces in 3D Polygonal Meshes Interpolation algorithms

2

## Слайд 2: Reminder: 2 D Curves 3

## Слайд 3: Curves in 3 D 4

## Слайд 4: Surfaces in 3 D 5

## Слайд 5: Surface Example: Planes in 3 D 6

## Слайд 6: Surface Example: Planes in 3 D 7

## Слайд 7: Topic 3

3D Objects General curves & surfaces in 3D Polygonal Meshes Interpolation algorithms

8

## Слайд 8: Polygonal Meshes 9

## Слайд 9: Polygonal Meshes 10

## Слайд 10: Why use polygon meshes? 11

## Слайд 11: Polygon Meshes

Set of edge-connected planar polygons (usually triangles or quads) Faces share vertices and edges To avoid repeating vertices, store each vertex once Each face stored as set of indices into the vertex list Connectivity of faces also called mesh topology Normal at vertex often estimated as average of unit normals of all faces sharing that vertex Useful in practice, but less precise than differentiating original surface

12

## Слайд 12: Topic 3

3D Objects General curves & surfaces in 3D Polygonal Meshes Interpolation algorithms

13

## Слайд 13: Controlling a curve

Specify control parameters at a few locations Points Tangents … Make the curve conform to these parameters 14

## Слайд 14: Interpolation with Splines

Want: Smooth curve through sequence of points Intuition: Generate the curve in parts, one between each pair of points This is called a spline curve Has local control (small change won’t affect whole curve) 15

## Слайд 15: Cubic Curve

P(t ) = at 3 + bt 2 + ct + d 4 degrees of freedom For instance, can be specified completely by 4 points on the curve Popular tradeoff between control and simplicity Multiple cubic segments can be linked together into a longer and more complex curve

16

## Слайд 16: Cubic Hermite Interpolation

Specify positions h 0, h 1 and tangents (slopes, derivatives) h 2, h 3 at two points: t = 0 and t = 1 17

## Слайд 17: Cubic Hermite interpolation

Q: Why tangents and not two extra points? A: When we want two curve segments to link up smoothly, we can just require them to have a common tangent at the boundary

18

## Слайд 18: Cubic Hermite Interpolation

P(t ) = at 3 + bt 2 + ct + d P’(t ) = 3at 2 + 2bt + c h 0 = P(0) = d h 1 = P(1) = a + b + c + d h 2 = P’(0) = c h 3 = P’(1) = 3a + 2b + c

19

## Слайд 19: Matrix Representation

h 0 = P(0) = d h 1 = P(1) = a + b + c + d h 2 = P’(0) = c h 3 = P’(1) = 3a + 2b + c 20

## Слайд 20: Matrix Representation 21

## Слайд 21: Matrix Representation of Polynomials  22

## Слайд 22: Matrix Representation of Polynomials 23

## Слайд 23: Hermite Basis Function 24

## Слайд 24: Catmull -Rom Interpolation

Want: Smooth curve through sequence of points Intuition: A plausible tangent at each point can be inferred directly from the data Now use Hermite Interpolation 25

## Слайд 25 26

## Слайд 26 27

## Слайд 27 28

## Слайд 28 29

## Последний слайд презентации: Topic 3 ### Похожие презентации

Ничего не найдено