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.

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Physical description of rendering

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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.

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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

• ne ray at the time.

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Colour

There are three types of cones in the human retina, with caraterstic re- sponse.

4000 ˚ A 5000 ˚ A 6000 ˚ A Relative response Wavelength

Red Green Blue

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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

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Lights

For the purpose of this lecture, we assume a simplified light model, where the light source is placed at infinity. VIS01

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Surface properties

Ambient lighting equation Rc = LcOc Diffuse lighting equation Rc = LcOc[ On · (− Ln)] and finally the specular part Rc = LcOc[ S · (− Cn)]Osp where S = 2[ On · (− Ln)] On +

• Ln. The complete lighting equation is thus

Rc = OaiOacLc − OdiOdcLc( On · Ln) + OsiOscLc[ S · (− Cn)]Osp VIS01

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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

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Cameras

The pictures below illustrates the terminology for cameras additionally we define a front and back clipping plane. VIS01

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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

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Homgeneous coordinates

We use homogeneous coordinates, so each point is represented by four values: (xh, yh, zh, wh) the corresponding 3D location is: x = xh wh y = yh wh z = zh wh Note that this representation includes points at infinity (wh = 0). VIS01

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Translation

A translation transform is defined by a matrix TT =

    

1 tx 1 ty 1 tz 1

    

applying this to (x, y, z, 1)T gives x′ = x + tx y′ = y + ty z′ = z + tz VIS01

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Scaling

Likewise We can scale an object by the transform matrix TS =

    

sx sy sz 1

    

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Rotation

Similary the rotation transform is given by TR =

     

cosθx′x cosθx′y cosθx′z cosθy′x cosθy′y cosθy′z cosθz′x cosθz′y cosθz′z 1

     

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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 {p1, p2, . . . , pn}, we would thus generate the actors coordinates in the world coordinate sys- tem as p′

i = TTTRTS pi

note that the order is very important! VIS01

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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

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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

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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

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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();

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Summary and outlook

Graphics systems will take care of the basics for us. The next step is to consider the visualization pipeline. VIS01