Anamorphism Transformation Geometry. Anamorphosis is a distorted projection or perspective requiring the viewer to use special devices or occupy a specific.

Slides:

Advertisements

Similar presentations

Geometry Point Line Line segment Ray Plane Parallel lines

Advertisements

Lecture 8 Transparency, Mirroring

Transformation Geometry

Three Dimensional Viewing

Reflection in Plane Mirrors Reflection in Plane Mirrors Objectives: Investigate reflection in plane mirrors Verify the “1st Law of Reflection” Compare.

MA Day 9 – January 17, 2013 Review: Equations of lines, Section 9.5 Section 9.5 –Planes.

Camera Models A camera is a mapping between the 3D world and a 2D image The principal camera of interest is central projection.

CS485/685 Computer Vision Prof. George Bebis

THE THIRD DIMENSION: DEPTH AND VOLUME. Projection All the objects, and their relationships, seen by the artist form the scene of the painting or the photograph.

Reflection Physics Department, New York City College of Technology.

CS223b, Jana Kosecka Rigid Body Motion and Image Formation.

Rendering Pipeline Aaron Bloomfield CS 445: Introduction to Graphics Fall 2006 (Slide set originally by Greg Humphreys)

10.3 Images in Concave Mirrors. Concave Mirror Unlike a plane mirror, a curved mirror produces an image that is a different size, shape, and/or orientation.

X y z Point can be viewed as intersection of surfaces called coordinate surfaces. Coordinate surfaces are selected from 3 different sets.

Images in Concave Mirrors. Properties  The mirror has a reflecting surface that curves inward.  When you look at objects in the mirror, the image appears.

Vectors: planes. The plane Normal equation of the plane.

Virtual reality. Tasks 3D digital model from planes 3D digital model of existing objects Office work Field observations Solid modeling Photogrammetry.

Images in Concave Mirrors. Properties  The mirror has a reflecting surface that curves inward.  When you look at objects in the mirror, the image appears.

MATH 306 Chapter 1.

Unit # 1 Vocabulary Review 1. coordinate plane 2.

Chapter 2 Section 2.4 Lines and Planes in Space. x y z.

Rendering Overview CSE 3541 Matt Boggus. Rendering Algorithmically generating a 2D image from 3D models Raster graphics.

CS 445 / 645: Introductory Computer Graphics Light.

Programming 3D Applications CE Displaying Computer Graphics Week 3 Lecture 5 Bob Hobbs Faculty of Computing, Engineering and Technology Staffordshire.

Opener New section For Notes… Reflections. Essential Question Learning Objective How can shapes be moved on a plane? Given a figure, I will perform.

Unit 4 – Flip, Slide & Turn Vocabulary. Unit 4 – Flip, Slide & Turn - Vocabulary Plane: One of the basic undefined terms of geometry. A plane goes on.

Reflection and Light Flat Mirrors.

Properties of Reflective Waves Flat Mirrors. Light travels in a straight line Some light is absorbed Some light is redirected – “Reflected”

CSE 681 Introduction to 3D Graphics. CSE 681 Computer graphics is “the creation and manipulation of graphics images by means of computer.” (Marc Berger,

Object image Reflection in Plane Mirrors Objectives: Investigate reflection in plane mirrors Verify the “1 st Law of Reflection” Compare image size and.

Computer Graphics Lecture 08 Fasih ur Rehman. Last Class Ray Tracing.

12/24/2015 A.Aruna/Assistant professor/IT/SNSCE 1.

Review from Friday The composition of two reflections over parallel lines can be described by a translation vector that is: Perpendicular to the two lines.

Rendering Pipeline Fall, D Polygon Rendering Many applications use rendering of 3D polygons with direct illumination.

Lesson 18Power Up DPage 114 Lines and Angles. Lines – No end, extends in both directions forever. Segments – Two endpoints, length can be measured. Lines.

CS 445 / 645: Introductory Computer Graphics Review.

1 Point Perspective, Aerial Perspective & 2 Point Perspective.

Unit 10 Transformations. Lesson 10.1 Dilations Lesson 10.1 Objectives Define transformation (G3.1.1) Differentiate between types of transformations (G3.1.2)

CSE 681 Introduction to Ray Tracing. CSE 681 Ray Tracing Shoot a ray through each pixel; Find first object intersected by ray. Image plane Eye Compute.

9.3 – Perform Reflections. Reflection: Transformation that uses a line like a mirror to reflect an image Line of Reflection: Mirror line in a reflection.

Parametric and general equation of a geometrical object O EQUATION INPUT t OUTPUT EQUATION INPUT OUTPUT (x, y, z)

Geometry 12-5 Symmetry. Vocabulary Image – The result of moving all points of a figure according to a transformation Transformation – The rule that assigns.

Mapping: Image Texturing CPSC 591/691. Texture Mapping Two-dimensional techniques place a two-dimensional (flat) image onto an object using methods similar.

L.E. February 22, 2016 Do Now : Take out notebook paper and date your notes today. Title it “ Pavement Chalk Art” Intro: Write your answers. What is public.

Projection. Conceptual model of 3D viewing process.

Computer Graphics Projections.

PROJECTIONS PROJECTIONS 1. Transform 3D objects on to a 2D plane using projections 2 types of projections Perspective Parallel In parallel projection,

Rendering Pipeline Fall, 2015.

3. Transformation

Reflections Geometry.

Transformations and Symmetry

PERSPECTIVE PROJECTION…...

Projection Our 3-D scenes are all specified in 3-D world coordinates

DESCRIPTIVE GEOMETRY The Descriptive Geometry turns 3D into

Rendering Pipeline Aaron Bloomfield CS 445: Introduction to Graphics

Foreshortening What is Foreshortening?

CSCE 441 Computer Graphics 3-D Viewing

Y. Davis Geometry Notes Chapter 9.

Law of Reflection θ(i) = θ(r) θ(i) θ(r)

TRANSFORMATIONS Translations Reflections Rotations

Work Features Work features are tools that help create and position features by providing points, lines, and planes when current geometry is not sufficient.

Module 2 Review

Reflections Geometry.

Starter page 10 Pick an object from your table.

Maps one figure onto another figure in a plane.

Work Features Work features are tools that help create and position features by providing points, lines, and planes when current geometry is not sufficient.

Presentation transcript:

Anamorphism Transformation Geometry

Anamorphosis is a distorted projection or perspective requiring the viewer to use special devices or occupy a specific vantage point to reconstitute the image Anamorphism – Is when artists foreshorten and angle linear perspective to deform and change the scale of an object. The image becomes incomprehensible when viewed directly but resolves into a clear picture when looked at from a different vantage point. There are two main types of anamorphism: perspective (oblique) and mirror (catoptric). Both perspectival and Mirror anamorphism date back to the Renaissance period. Perspectival anamorphism - requires the viewer to look at a picture from an unusual angle instead of standing in front of the painting and looking at it straight on. Mirror anamorphism - a conical or cylindrical mirror is placed on the drawing or painting to transform a flat distorted image into a three-dimensional picture that can be viewed from many angles.

Perspectival anamorphism

Mirror anamorphism

Where is the Math in Mirror Anamorphosis Find equation for surface Define vector from viewer to pixel Find intersection Calculate normal vector Find reflection vector Determine printing coordinates

The Set-Up

Finding the intersection

Finding the Normal Vector A normal vector is a vector perpendicular to another object, such as a surface or plane. Often we refer to a unit normal vector as n.

Finding the Reflection Vector a Reflection is a mapping from a Euclidean space to itself. The image of a figure by a reflection is its mirror image in the axis or plane of reflection.

Printing the Pixel

Future work on anamorphs of 3D models will include investigating what can be done with conical and cylindrical anamorphs in combination with their respective reflecting surface and a ray tracing rendering. Anamorphic texture mapping might be interesting to persue also. Other collineations could be explored.

Sources libraries.org/ehost/pdfviewer/pdfviewer?vid=6&sid=b351ca af56-cec f7%40sessionmgr113&hid=123 libraries.org/ehost/pdfviewer/pdfviewer?vid=6&sid=b351ca af56-cec f7%40sessionmgr113&hid= washpresentation.pdf washpresentation.pdf