2000-01-16 - Part 2 Lecture 3: Computer graphics Introduction - PowerPoint PPT Presentation

Mats Nyl´ en January 16, 2001 Slide 1 of 21 2000-01-16 - Part 2 • Lecture 3: Computer graphics – Introduction – Colour, Lights & Surface properties – Cameras & Coordinate systems • Lecture 4: Computer graphics cont’d – Coordinate transformations & Actor geometry – Graphics systems – A simple vtk example • Textbook: Chapter 3, except 3.10 which is covered in lecture 11. • Exercises: 3.1, 3.2, 3.7 and 3.8. VIS01

Mats Nyl´ en January 16, 2001 Slide 2 of 21 Physical description of rendering VIS01

Mats Nyl´ en January 16, 2001 Slide 3 of 21 Image-order and object-order There are two types of rendering algorithms • Image order , e.g., ray-tracing (or ray-casting) • Object order , render one object at a time. VIS01

Mats Nyl´ en January 16, 2001 Slide 4 of 21 Surface versus volume rendering When we think about rendering we often think about surface-rendering, however some things are very hard to do with that kind of technique, e.g., clouds, smoke or translucent surfaces. This leads to the idea of Volume rendering . Volume-rendering is naturally done with ray-tracing or ray-casting techniques, where rendering is done one ray at the time. VIS01

Mats Nyl´ en January 16, 2001 Slide 5 of 21 Colour There are three types of cones in the human retina, with caraterstic re- sponse. Green Red Blue Relative response 4000 ˚ A 5000 ˚ 6000 ˚ A A Wavelength VIS01

Mats Nyl´ en January 16, 2001 Slide 6 of 21 Colour models There are various colour models in use • RGB specifies colours as an additive mix of Red, Green and Blue. • HSV Specfies Hue (colour), Saturation, and Value to specify a colour. • CMY specifies colours as a subtractive mix of Cyan, Magenta and Yel- low, this colour model is mainly used for printing purposes. VIS01

Mats Nyl´ en January 16, 2001 Slide 7 of 21 Lights For the purpose of this lecture, we assume a simplified light model, where the light source is placed at infinity. VIS01

Mats Nyl´ en January 16, 2001 Slide 8 of 21 Surface properties Ambient lighting equation R c = L c O c Diffuse lighting equation R c = L c O c [ � O n · ( − � L n )] and finally the specular part C n )] O sp R c = L c O c [ � S · ( − � where � S = 2[ � O n · ( − � L n )] � O n + � L n . The complete lighting equation is thus C n )] O sp R c = O ai O ac L c − O di O dc L c ( � O n · � L n ) + O si O sc L c [ � S · ( − � VIS01

Mats Nyl´ en January 16, 2001 Slide 9 of 21 Effects of specular reflection The following figure illustrates the effect of the specular component. The toprow has a specular intensity value of 0.5, and the bottom row 1.0. The specular exponent is 5, 10, 20 and 40 VIS01

Mats Nyl´ en January 16, 2001 Slide 10 of 21 Cameras The pictures below illustrates the terminology for cameras additionally we define a front and back clipping plane. VIS01

Mats Nyl´ en January 16, 2001 Slide 11 of 21 Coordinate systems There are four distinct coordinate systems commonly used in computer graphics: model , world , view and display . • the model coordinate system is where the model is defined, one for each actor • the world coordinate system is the 3D system within which the actors are placed • the view coordinate system is what is visible in the camera, each point having a x and y value as well as a depth, or z value. • the display coordinate system is in actual pixels on the screen VIS01

Mats Nyl´ en January 16, 2001 Slide 12 of 21 Homgeneous coordinates We use homogeneous coordinates , so each point is represented by four values: ( x h , y h , z h , w h ) the corresponding 3D location is: x = x h y = y h z = z h w h w h w h Note that this representation includes points at infinity ( w h = 0). VIS01

Mats Nyl´ en January 16, 2001 Slide 13 of 21 Translation A translation transform is defined by a matrix   1 0 0 t x 0 1 0 t y   T T =   0 0 1 t z     0 0 0 1 applying this to ( x, y, z, 1) T gives x ′ = x + t x y ′ = y + t y z ′ = z + t z VIS01

Mats Nyl´ en January 16, 2001 Slide 14 of 21 Scaling Likewise We can scale an object by the transform matrix  0 0 0  s x 0 0 0 s y   T S =   0 0 0 s z     0 0 0 1 VIS01

Mats Nyl´ en January 16, 2001 Slide 15 of 21 Rotation Similary the rotation transform is given by   0 cosθ x ′ x cosθ x ′ y cosθ x ′ z 0 cosθ y ′ x cosθ y ′ y cosθ y ′ z     T R =   0 cosθ z ′ x cosθ z ′ y cosθ z ′ z     0 0 0 1 VIS01

Mats Nyl´ en January 16, 2001 Slide 16 of 21 Complete transform To transform the coordinates of an actor we would 1 scale the actor 2 rotate the actor 3 translate the actor If the actor is defined by a series of (homogeneous) coordinates { p 1 , p 2 , . . . , p n } , we would thus generate the actors coordinates in the world coordinate sys- tem as p ′ i = T T T R T S p i note that the order is very important! VIS01

Mats Nyl´ en January 16, 2001 Slide 17 of 21 Graphics Systems Typical graphics system will render a few simple graphics primitives in an efficient fashion • Polygon • Triangle strip • Line • Polyline • Point On high end system all of these will be rendered in hardware. VIS01

Mats Nyl´ en January 16, 2001 Slide 18 of 21 Shading alternatives When rendering surfaces, smooth surfaces are replaced with polygonal ap- proximations, to regain the smooth appearance som sort of shading needs to be done • Flat shading: the normal used in the lighting calculation is the actual normals of the polygons • Goroud shading: uses normals at each vertex, then interpolates during scan-conversion • Phong shading: interpolates the vertex normals for each point within the polygon. Hardware Phong shading will soon be a standard feature. VIS01

Mats Nyl´ en January 16, 2001 Slide 19 of 21 A simple example Let us the object-oriented graphics of vtk to create a simple scene consist- ing of a single cone. We will need these classes vtkRenderer vtkRenderWindow vtkConeSource vtkPolyDataMapper vtkActor VIS01

Mats Nyl´ en January 16, 2001 Slide 20 of 21 Main part of program // create a rendering window and renderer vtkRenderer *ren = vtkRenderer::New(); vtkRenderWindow *renWindow = vtkRenderWindow::New(); renWindow->AddRenderer(ren); renWindow->SetSize( 300, 300 ); // create an actor and give it cone geometry vtkConeSource *cone = vtkConeSource::New(); cone->SetResolution(8); vtkPolyDataMapper *coneMapper = vtkPolyDataMapper::New(); coneMapper->SetInput(cone->GetOutput()); vtkActor *coneActor = vtkActor::New(); coneActor->SetMapper(coneMapper); // assign our actor to the renderer ren->AddActor(coneActor); // draw the resulting scene renWindow->Render(); VIS01

Mats Nyl´ en January 16, 2001 Slide 21 of 21 Summary and outlook Graphics systems will take care of the basics for us. The next step is to consider the visualization pipeline. VIS01