'Homogeneous coordinates' diaporamas de présentation

More details and examples on robot arms and kinematics

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Fitting a transformation: feature-based alignment

Fitting a transformation: feature-based alignment. Thursday, September 26 th 2013 Devi Parikh Virginia Tech.

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Image alignment

Image alignment. Image from http://graphics.cs.cmu.edu/courses/15-463/2010_fall/. A look into the past. http://blog.flickr.net/en/2010/01/27/a-look-into-the-past/. A look into the past. Leningrad during the blockade. http://komen-dant.livejournal.com/345684.html. Bing streetside images.

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Image Warping

621 views • 54 slides

2-D Geometry

2-D Geometry. The Image Formation Pipeline. Outline. Vector, matrix basics 2-D point transformations Translation, scaling, rotation, shear Homogeneous coordinates and transformations Homography, affine transformation. Notes on Notation (a little different from book).

865 views • 46 slides

2-D Geometry

2-D Geometry. The Image Formation Pipeline. Outline. Vector, matrix basics 2-D point transformations Translation, scaling, rotation, shear Homogeneous coordinates and transformations Homography, affine transformation. Notes on Notation (a little different from book).

582 views • 46 slides

Chapter 4

Chapter 4. Geometric Objects and Transformation. Lines. Consider all points of the form P( a )=P 0 + a d Set of all points that pass through P 0 in the direction of the vector d. Parametric Form. This form is known as the parametric form of the line

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Foundations of Computer Graphics ( Fall 2012)

Foundations of Computer Graphics ( Fall 2012). http:// inst.eecs.berkeley.edu /~cs184. CS 184, Lecture 4: Transformations 2. To Do. Start doing HW 1 Time is short, but needs only little code [Due Wed Sep 12] Ask questions or clear misunderstandings by next lecture Specifics of HW 1

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Computer Graphics (fall 2009)

Computer Graphics (fall 2009). School of Computer Science University of Seoul. Chap 5: Viewing. Classical and Computer Viewing Viewing with a Computer Positioning of the Camera Simple Projections Projections in OpenGL Hidden-Surface Removal Interactive Mesh Displays

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Multiple View Geometry

Multiple View Geometry. Marc Pollefeys University of North Carolina at Chapel Hill. Modified by Philippos Mordohai. Tutorial outline. Introduction Visual 3D modeling Acquisition of camera motion Acquisition of scene structure Constructing visual models Examples and applications .

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Projective 2D & 3D geometry course 2

Projective 2D & 3D geometry course 2. (x,y,1). image plane. The projective plane. Why do we need homogeneous coordinates? represent points at infinity, homographies, perspective projection, multi-view relationships What is the geometric intuition?

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Mathematical Topics

Mathematical Topics . Review of some concepts: trigonometry aliasing coordinate systems homogeneous coordinates matrices, quaternions. Vectors. v = ai + bj + ck Describes point or displacement in n-dimensional space Addition, subtraction Multiplication scalar times vector

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Overview

Overview. Goals of the course: 1. to introduce real-time 3D graphics programming with openGL 2. to explore some mathematical foundations of graphics algorithms Projects: 1. One or two problem sets 2. A research project 3. A short animated visualization (for the End of the Year show)

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Single-view geometry

Single-view geometry. Odilon Redon, Cyclops , 1914. X?. X?. X?. Our goal: Recovery of 3D structure. Recovery of structure from one image is inherently ambiguous. x. Our goal: Recovery of 3D structure. Recovery of structure from one image is inherently ambiguous.

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Homogeneous Coordinates (Projective Space)

Homogeneous Coordinates (Projective Space). Let be a point in Euclidean space Change to homogeneous coordinates: Defined up to scale: Can go back to non-homogeneous representation as follows:. 3-D Transformations: Translation.

538 views • 22 slides

CS 378: Computer Game Technology

CS 378: Computer Game Technology. 3D Engines and Scene Graphs Spring 2012. Representation. We can represent a point , p = (x,y), in the plane as a column vector as a row vector. Representation, cont. We can represent a 2-D transformation M by a matrix

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2D Geometric Transformations

2D Geometric Transformations. Graphics Systems / Computer Graphics and Interfaces. 2D Geometric Transformations.

667 views • 19 slides

Chapter 3: Geometric Objects and Transformations

Chapter 3: Geometric Objects and Transformations. Vectors and Matrices Dot Products Cross Products Affine Transformations Rotation, Scaling, and Translation Homogeneous Coordinates. Vectors and Matrices 2D Parametric Equations.

330 views • 15 slides

Geometric Transformations

Geometric Transformations. CSE 455 Ali Farhadi. Many slides from Steve Seitz and Larry Zitnick. What are geometric transformations?. Translation. Preserves: Orientation. Translation and rotation. Scale. Similarity transformations.

277 views • 15 slides

Geometric Transformations

Geometric Transformations. CSE P 576 Larry Zitnick (larryz@microsoft.com). What are geometric transformations?. Translation. Translation and rotation. Scale. Similarity transformations. Similarity transform (4 DoF ) = translation + rotation + scale. Aspect ratio. Shear.

276 views • 15 slides