1. Virtual reality

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

3. Solid modeling From 2D elements Body representation methods Cross section and a vector (sweeping) Cross section and a axis of rotation (body of revolution) Constructive Solid Geometry (CSG) Boundary representation (BR) Voxels

4. Creating 3D world Difficulties using 2D tools CAD or special software (3D Studio) Constructing from views (front view, top view, side view) Different views at the same time (perspective, front, top, views) Primitive objects (box, sphere, cone, cylinder, etc.) 3D faces, surfaces (NURBS, Non Uniform Rational B-Splines) Materials, texture maps, material libraries

5. NURBS Non Uniform Rational B-Splines

6. Vizualization Hidden lines, hidden surfaces Z-buffer algorithm ray traceing reflection, transparency Wireframe Rendering, light sources, materials

7. Digital model from photos object photo f t x x’ photo II x” object photo x’ x Constant scale factor Scale factor changing

8. Projective transformation Perspective projection between two non parallel planes, collinarity condition Form with homogeneous coordinatas Two linear equation for each point Homogeneous coordinates

9. Projective transformation

10. Spatial solution (3D) Relative orientation, minimum. 6 points on both photos, reconstructing the relative position Two photos from different point of views Absolute orientation, minimum 3 known points in the used co-ordinate system Analytical solution (mathematical projection, adjustment) Connecting several photos to the model

11. Measuring control points Intersection Polar points (Direct reflex) Laser scanner Robotic instruments

12. VRML Virtual Reality Markup Language Free viewers http://www.parallelgraphics.com/products/cortona/ Cortona VRML Client VRML 1 1995 (Silicon Graphics' Open Inventor ASCII format) VRML 2 1996 Cosmo Player VRML 97 (ISO/IEC-14772-1:1997).wrl files (world) Simple text files, platform independent #VRML V2.0 utf8 Shape { geometry Box { size 1 1 1 }

13. VRML cont. VRML features Description of 3D spaces (creation?) Moving objects, animation Hyperlinks (html, wrl) Playing sound and video User interactivity Programmable (java or javascript) Application areas Visual design, cities, flats, etc. Advertisements, games, artist Education (geometry) Tourism (virtual cities) Simulation, mechanical engineering Vrml.html