中国科学技术大学：《数字几何处理 Digital Geometry Processing》课程教学资源（课件讲义）01 Representation

Representations Xiao-Ming Fu

Outline Point cloud Signed distance field Implicit function Grid Pixel, Voxel ◇ Quad-tree, Octree Mesh Triangle, Tetrahedron Data structure Halfedge File format Obj, Off

Point cloud Xi P={P1,,PN,},pi= ER3 Zi 3D scanners A set of data points in some coordinate system

𝒫 = {𝒑1, … , 𝒑𝑁𝑣 }, 𝒑𝑖 = 𝑥𝑖 𝑦𝑖 𝑧𝑖 ∈ ℛ3 A set of data points in some coordinate system 3D scanners

Applications scanners ◇Reverse engineering Physical Part Generate Scan Data Create Mesh Finished Assembly Modeling Process Region Group

Applications scanners Digital preservation of cultural heritage sites and objects 009

Depth camera Depth camera:Kinect,RealSense,IPhone X,..... 00 (intel> XBOX 360 REALSENSE H N O L

Depth camera Ambient light sensor Speaker True Depth Camera Proximity sensor Microphone Flood Illuminator 7MP camera Infrared camera Dot projector

True Depth Camera

Depth Image Gray image:pixel represents distance from camera. Real capture by Kinect. Nearer is brighter. Nearer is darker

Gray image: pixel represents distance from camera. Nearer is brighter. Real capture by Kinect. Nearer is darker

Outline ◇Point cloud Signed distance field ◇Implicit function ◇Grid ◇Pixel,Voxel ◇Quad-tree,Octree ◇Mesh Triangle,Tetrahedron Data structure Halfedge File format ◇Obj,Off

Signed distance field The distance of a given point x from the boundary of fx)= (-d(x,as), ifx∈2 d(x,a2), ifx∈nc Contour line

Contour line Ω