CS 325Introduction to Computer Graphics

03 / 29 / 2010

Instructor: Michael Eckmann

Michael Eckmann - Skidmore College - CS 325 - Spring 2010

Today’s Topics• Questions?

• Program 3 comments

• Surface Rendering / Shading models

– Flat

– Gouraud

– Phong

• Ray tracing

– Ray Sphere intersections

– Ray Polygon intersections

Michael Eckmann - Skidmore College - CS 325 - Spring 2010

Program 3 comments• Let's consider the steps you need to go about getting an object

specified in 3d to be shown on screen.

• NOTE WELL: Whatever min/max x,y coordinates you specify in gluOrtho2d, that is the window in WORLD coordinates that will be displayed in your viewport.

Michael Eckmann - Skidmore College - CS 325 - Spring 2010

Illumination• Illumination models are used to calculate the color of a point on

the surface of an object.

• A surface rendering (aka shading) method uses the calculations from the illumination model to determine the pixel colors of all the projected points in a scene.

– Can be done by doing illumination model calculations at each pixel position (like you'll see is done in ray tracing).

OR

– Can be done by doing a small number of illumination calculations and interpolating between pixels (like is often done in scan line algorithms.)

Surface Rendering• Now that we have an illumination model built, we can use it in different

ways to do surface rendering aka shading.

Shading Models• Constant shading (aka flat shading, aka faceted shading) is the simplest

shading model.

• It is accurate when a polygon face of an object is not approximating a

curved surface, all light sources are far and the viewer is far away from

the object. Far meaning sufficiently far enough away that N • L and R •

V are constant across the polygon.

• If we use constant shading but the light and viewer are not sufficiently far

enough away then we need to choose a value for each of the dot products

and apply it to the whole surface. This calculation is usually done on the

centroid of the polygon.

• Advantages: fast & simple

• Disadvantages: inaccurate shading if the assumptions are not met.

Shading Models• Interpolated shading model

– Assume we're shading a polygon. The shading is interpolated

linearly. That is, we calculate a value at two points and interpolate

between them to get the value at the points in between --- this saves

lots of computation (over computing at each position) and results in a

visual improvement over flat shading.

– This technique was created for triangles e.g. compute the color at the

three vertices and interpolate to get the edge colors and then

interpolate across the triangle's surface from edge to edge to get the

interior colors.

– Gouraud shading is an interpolation technique that is generalized to

arbitrary polygons. Phong shading is another interpolation technique

but doesn't interpolate intensities.

Shading Models• Gouraud shading (aka Gouraud Surface Rendering) is a form of

interpolated shading.

– How to calculate the intensity at the vertices?

• we have normal vectors to all polygons so, consider all the

polygons that meet at that vertex. Drawing on the board.

• Suppose for example, n polygons all meet at one vertex. We

want to approximate the normal of the actual surface at the

vertex. We have the normals to all n polygons that meet there.

So, to approximate the normal to the vertex we take the average

of all n polygon normals.

• What good is knowing the normal at the vertex? Why do we

want to know that?

Shading Models• Gouraud shading.

– What good is knowing the normal at the vertex? Why do we want to

know that?

• so we can calculate the intensity at that vertex from the

illumination equations.

– Calculate the intensity at each vertex using the normal we estimate

there.

– Then linearly interpolate the intensity along the edges between the

vertices.

– Then linearly interpolate the intensity along a scan line for the

intensities of interior points of the polygon.

– Example on the board.

Shading Models• Advantages: easy to implement if already doing a scan line algorithm.

• Disadvantages:

– Unrealistic if the polygon doesn't accurately represent the object.

This is typical with polygon meshes representing curved surfaces.

– Mach banding problem

• when there are discontinuities in intensities at polygon edges, we

can sometimes get this unfortunate effect.

• let's see an example.

– The shading of the polygon depends on its orientation. If it rotates,

we will see an unwanted effect due to the interpolation along a

scanline. Example on board.

– Specular reflection is also averaged over polygons and therefore

doesn't accurately show these reflections.

Shading Models• Phong shading (aka Phong Surface Rendering).

– Assume we are using a polygon mesh to estimate a surface.

– Compute the normals at the vertices like we did for Gouraud.

– Then instead of computing the intensity (color) at the vertices and

interpolating the intensities, we interpolate the normals.

– So, given normals at two points of a polygon, we interpolate over the

surface to estimate the normals between the two points.

– Example picture on the board.

– Then we have to apply the illumination equation at all the points in

between to compute intensity. We didn't have to do this for Gouraud.

– Problems arise since the interpolation is done in the 3d world space

and the pixel intensities are in the image space.

– More accurate intensity value calculations, more realistic surface

highlights and reduced Mach banding.

Shading Models• Recap

– Flat Shading

– Gouraud Shading --- interpolates intensities

– Phong Shading --- interpolates normal vectors (before calculating

illumination.)

– For these three methods, as speed/efficiency decreases, realism

increases (as you'd expect.)

– They all have the problem of silhouetting. Edges of polygons on the

visual edge of an object are apparent.

– Let's see examples of Gouraud and Phong shading.