Georg Petschnigg - Image Synthesis

CS 348b - Image Synthesis Homework Page

This is the homework page of Georg Petschnigg for Stanford's Image Synthesis course.
Jump to Homework: 1 2 3 Final Project Page

Homework 1

The main goal of homework 1 was to familiarize myself with lrt - the literate raytracer. Here are the results.

What physical quantity do we measure along a ray?
First we measure the distance of the intersection point and ray origin and the we integrate the spectral power density along the ray, This corresponds to the contribution of this particular point in the final image.
What lrt class is used to describe the reflection of light at a point?
In order to describe the reflection of light at a point, lrt uses a class called BSDF or “Bidirectional Scattering-Distribution Function”.
How are vectors and normals treated differently?
Normals do not transform the same way as vectors do. If a sphere is non uniformly scaled for example, the surface normal can not be treated as a direction. Mathematically a normal is the cross product of two surface tangent vectors. Tangents and vectors can be transformed with a standard transformation matrix. Normals however, have to be transformed using the inverse transpose of the transformation matrix.
What's the difference between Intersect and IntersectP?
Shape::Intersect, returns information about a a single ray-shape intersection corresponding to the intersection closest to the ray origin. The other, Shape::IntersectP simply tells the caller whether or not an intersection occurs, without specifying any details about the nature of the intersection itself. The IntersectP routine is almost identical to Intersect, but it does not fill in the DifferentialGeometry structure, nor does it update the ray’s maxt field.
How is the information about intersection between a ray and a shape represented in lrt?
Intersect returns a boolean indicating whether the shape was hit, and information about the hit if an intersection occurs. The hit itself is not represented as a point, but rather as a small patch on the surface. This information is stored in a DifferentialGeometry structure, that includes position, normal, and tangents to the surface and surface parameters.
What kind of coordinates are used to parameterize a triangle?
Barycentric coordinates are used to parameterize a triangle in terms of two variables, u and v.

Here is a first rendering of my name:

Homework 2

For homework two we had to extend an existing raytracer called lrt so that height fields would render more efficiently. Finally the reflection and shading of the geometry of the objects should be "phong" interpolated. This means object surface lighting would appear "smoother", Here are some sample Images.

Original Version - crude faceted triangles visible

After changes - triangles are smoothly shaded

A more efficient algorithms runs about twice as fast

This image contains about 2 Million triangles

Homework 3

Homework three's assignment was to implement a "realistic" camera model for the lrt ray tracer. First we had to implement depth of field effects, which are due to the finite aperture size of a real camera. This causes objects which do not lie on the image plane to become blurred. Here is an example:

Depth of Field
Camera Settings ---------------------------------- Camera Mode: aperture_priority Shutter Speed: 1/30sec Focal Length: 1 F-Stop: F0.5 Aperture: 2 FOV: 45 degrees Autofocus: ON Sample Coords: 91 100 Focal Distance: 8.97172 Film gain: 37.892

In this image the camera is focused on the green cone. The blue and red cone do not lie on the image plane and are thus blurred.

The second effect we had to implement was motion blur which is caused by camera or object motion during a shot.

Motion Blur

Camera Settings ---------------------------------- Camera Mode: shutter_priority Shutter Speed: 1/0.2sec Focal Length: 2 F-Stop: F12 Aperture: 0.166667 FOV: 45 degrees Autofocus: ON Sample Coords: 91 100 Focal Distance: 8.97172 Film gain: 37.5807

The final step was to implement an automatic focus and exposure system. I implemented to following approach:

Auto Focus
The algorithm attempts casts test rays starting from the center, alternating left and right in ever increasing steps, until and object is hit. If no object is hit in a scan line, the next scan line above, then below is tested, and so on until there are not scan lines left. Once an intersection has occurred the image plane is placed at that depth (example).
Automatic Exposure
Instead of implementing an error prone exposure heuristic, I decided to tweak the film sensitivity to match the illumination of the scene. This step is performed posteriori after all the image sample have been computed. I find the largest R, G, or B value and set the image gain to be the inverse of the maximum RGB value. This way each sample is guaranteed to be within the 0 - 1 range. This approach breaks down if a intentionally dark scene is rendered, or if an overly large dynamic range is required. In the end I favored this approach, because to bright images can be easily corrected for.
Shutter Priority Mode
In this mode the focal distance and film gain are set as described above. The shutter speed is given by the user. The focal length is fixed to 2 and the F-Stop is set to 12. I chose these values to reflect the aperture to mimic traditional 35mm film camera settings. This mode gives the user full control over exposure time allowing him or her to experiment with motion blur effects.
Aperture Priority Mode
Here again focal distance and film gain are automatically set. In this case however the user has full control over the aperture size. This allows for uninhibited depth of field effect exploration. The exposure time is set to 1/30sec which as a rule of thumb is the largest exposure time before a tripod is necessary.
Programmed Mode
In this mode every setting is adjusted automatically. The film gain and focal distance are set as described above. The shutter speed is fixed to 1/30sec, F-Stop to F12 and the focal length at 1. This mode comes close to the "point & shoot" operation of a pocket camera (example).

Auto-focus selects Blue Cone

Camera Settings ---------------------------------- Camera Mode: programmed Shutter Speed: 1/30sec Focal Length: 1 F-Stop: F12 Aperture: 0.0833333 FOV: 45 degrees Autofocus: ON Sample Coords: 37 100 Focal Distance: 13.2744 Film gain: 37.9423

Auto-focus selects Red Cone

Auto-focus selects center first

Camera Settings ---------------------------------- Camera Mode: programmed Shutter Speed: 1/30sec Focal Length: 1 F-Stop: F12 Aperture: 0.0833333 FOV: 33 degrees Autofocus: ON Sample Coords: 87 100 Focal Distance: 8.89726 Film gain: 37.9462

Auto-focus selects Blue Cone

Original Version - crude faceted triangles visible	After changes - triangles are smoothly shaded
A more efficient algorithms runs about twice as fast	This image contains about 2 Million triangles