bedrich benes, ph.d. representation purdue...

CGT 101GeometryBedrich Benes, Ph.D.Purdue UniversityDepartment of Computer Graphics Technology andDepartment of Computer Science

© Bedrich Benes

Objects in Computer Graphics

• Boundary representation

• Volumetric representation

• Point clouds

© Bedrich Benes

Boundary representations

© Bedrich Benes

Boundary representation

• Objects are empty

• Represented by their boundary

• Also called B‐rep [bee rep]

© Bedrich Benes

B‐rep

© Bedrich Benes

B‐reps• There are various types of B‐reps

• Analytic (free form) – used in CAD/CAM

• Polygonal – used in real‐timeapplications (games, VR, …)

© Bedrich Benes

Analytic Representation• The boundary is expressed by an equation

‐ circle in 2D

‐ sphere in 3D

© Bedrich Benes

Analytic Representation

© Bedrich Benes

Free‐form Surfaces• Bézier surfaces• NURBS• Subdivision Surfaces

• Allow for complex forms• May be difficult to control

© Bedrich Benes

Bézier Surfaces

© Bedrich Benes

Mesh of Triangles

• The most common representation is by triangular meshes

• Triangle is a simplex (planar, convex)

• Mesh of triangles

© Bedrich Benes

Mesh of Triangles

© Bedrich Benes

Sources of B‐rep Data• How can we get polygonal meshes?

• From free‐form surfaces by tessellation • From existing sources on the internet

www.thingiverse.com

© Bedrich Benes

www.thingiverse.com

© Bedrich Benes

Sources of B‐rep Data• How can we get polygonal meshes?

• From free‐form surfaces by tessellation • From existing sources on the internet

www.thingiverse.com• From scanning real‐world objects

© Bedrich Benes

Scanned Barcelona

© Bedrich Benes




• Image‐based representation (imposters)

• Point clouds© Bedrich Benes

Volumetric representations

© Bedrich Benes

Voxels• Voxel is an acronym for volume element • A pixel is an enumeration of 2D plane

a voxel is an enumeration of 3D space• A voxel is NOT a little cube!

It is a value of a 3D array• Displaying depends on the application• Minecraft uses cubes…

https://softologyblog.wordpress.com/2017/05/27/voxel-automata-ter

© Minecraft © Bedrich Benes

Voxels• The voxel value depends on the application:

density, temperature, pollution intensity,…

• Application areas:medicine, meteorology, astronomy, geology, etc.

© Bedrich Benes

Volumetric rendering

© Bedrich Benes

Weather, clouds, particles

© l3wk

© Bedrich Benes

VoxelsThere are three main problems:

1) data size ‐ data is large

2) data acquisition ‐ we must see inside

3) data visualization ‐ how can we display it?

© Bedrich Benes

VoxelsExample:Wood log scannedin 512x512x1024What is the data size?

512x512x1024=268,435,456 B==262,133 kB=256MB

© Bedrich Benes

VoxelsExample 2:Two hours of weather data in resolution 512x512x512. One sample per minute

One sample: 512x512x512=134,217,728B==128MBTwo hours:128MBx120=15GB

© Bedrich Benes

Weather data

© Bedrich Benes

Voxels ‐ DisplayingDirect Volume Rendering (DVR)

• The volume is directly displayed

• Today, by raycasting on the GPU

© Bedrich Benes

Voxels ‐ Displaying• Raycasting

A ray is sent from the viewpoint (camera) It penetrates the volume and traverses through it

• What value is used for displaying?

© Bedrich Benes

Voxels ‐ Displaying• Raycasting

(C) Petr Felkel © Bedrich Benes

Voxels ‐ DisplayingFirst hit (the surface) Integrated value of

the volume on theray (sum) X‐ray

(C) Petr Felkel

© Bedrich Benes

Sources of Volumetric DataSpecialized devices

• CT scanners

• Doppler radars (C) www.history.com

© Bedrich Benes




• Point clouds

© Bedrich Benes

Point clouds

© Bedrich Benes

Point clouds• Unstructured sets of 3D points

e.g.,

• The value can be binary or a color (texture)

• They usually server as an intermediate representation for further processing

© Bedrich Benes

Example

http://mypointclouds.com/ © Bedrich Benes

Point clouds• Unstructured sets of 3D points

• What is the underlying structure?

Depends on the area• Architecture? • Weather?• Biology?

© Bedrich Benes

Point clouds• Point cloud reconstruction

• An open problem

© Hein A M Daanen© Bedrich Benes

Sources of Point Clouds• Some algorithms• Structure From Motion (SfM)

allows for creation of a point cloud from sequence of images

• Record a video, software converts to point cloud• Colmap https://colmap.github.io/• Visual SFM http://ccwu.me/vsfm/

© Bedrich Benes

Example from Visual SFM• Take a cell phone• Record video• Convert to images

• Match and reconstruct

© Bedrich Benes

Example from Visual SFM

© Bedrich Benes

SFM• Structure from Motion

• Time consuming (two hours on i9‐9900k @ 5GHz, Titan X)

• Requires a lot of data

• Can be helped with GPU© Bedrich Benes

Lidar• Light Detection and Ranging• $1k‐$100k (2019)• Can be

• Airborne (drone, airplane)• Terrerstrial• Mounted on a car

• Provides Point Clouds

By David Monniaux - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=1730946

© Bedrich Benes

Lidar• Sends a laser pulse• Measures the time

to record it as the frequency shift

• The is converted to distance• GPS – location, IMU ‐ orientation• Lidars are increasingly available

© Lidar technology, Inc.

© Bedrich Benes

Lidar• Lidars are used in (self‐driving) cars• Can sense the environment

© Argo AI

bedrich benes, ph.d. representation purdue...

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