[Indigo]<Solidviews>Models>Shading.mesa!6

File: Shading.mesa

Last edited by Bier on May 23, 1985 11:00:35 pm PDT

Contents: A camera model for shading surfaces, given surface type, lighting conditions and aperture size. No attempt is made to provide finite depth of field or other artifacts of a real camera.

Frank Crow added Utah-style highlights on September 23, 1982 12:22 pm

DIRECTORY

GraphicsColor,

Rope,

SV3d,

SVModelTypes,

SVVector3d;

Shading: DEFINITIONS =

BEGIN

Given a surface normal and the vector to the light source (we assume the light source is far compared to the diameter of a sphere containing the whole scene, so that this light source vector can be considered a constant), and given a surface type and light source type, we can find the radiance of the surface (R in watts/meter^2). Then, given the aperture size and the distance of the object from the aperture, we can find the solid angle of the aperture (OmegaAperture in steradians = (area of aperture)/(radius^2)). If we assume that the viewer is far from the scene compared to the diameter of a sphere containing the scene so radius is roughly constant over the scene then OmegaAperture depends only on the area of the aperture (meters^2). We are interested in the Irradiance (E) of our "film" (The screen or printer). This is just E = R*OmegaAperture (watts/meter^2).

To complete the cameral model, we would need to consider exposure time and film sensitivity, but, I will pretend that the film is a screen which sends to the viewer all of the power it receives.

A further discussion of rediometric terms appears in my paper (An Image Understanding Primer, MIT 1982) pp. 21 - 23, or see Horn, Berthold K. P. and Sjoberg, Robert W.. "Calculating the Reflectance Map," AIMemo 498, MIT AI Lab, October 1978.

Color: TYPE = GraphicsColor.Color;

LightSource: TYPE = SVModelTypes.LightSource;

LightSourceList: TYPE = SVModelTypes.LightSourceList;

Vector: TYPE = SVVector3d.Vector;

Point3d: TYPE = SV3d.Point3d;

CollimatedLambertianRadiance: PROCEDURE [surfaceNormal: Vector, lightSource: LightSource, albedo: REAL ← 1] RETURNS [radiance: REAL];

Collimated light source at lightSource. Lambertian surface with given albedo (0 to 1) oriented by given surfaceNormal.

DiffuseReflectance: PUBLIC PROCEDURE [surfaceNormal: Vector, surfacePt: Point3d, surfaceColor: Color, lightSources: LightSourceList] RETURNS [completeColor: Color];

DiffuseAndSpecularReflectance: PROCEDURE [eyePoint: Point3d, surfaceNormal: Vector, surfacePt: Point3d, surfaceColor: Color, lightSources: LightSourceList] RETURNS [color: Color];

Frank Crow's highlighted intensity model

CollimatedSpecularRadiance: PROCEDURE [surfaceNormal: Vector, lightSource: LightSource, albedo: REAL ← 1] RETURNS [radiance: REAL];

Collimated light source at lightSource. Specular surface with given albedo oriented by given surfaceNormal.

SimpleFilmIrradiance: PROCEDURE [radiance: REAL, omegaAperture: REAL] RETURNS [irradiance: REAL];

SolidAngle: PROCEDURE [surfacePoint: Point3d, areaAperture: REAL] RETURNS [omegaAperture: REAL];

Assumes aperture at [0,0,0];

LamFilmIrradiance: PROCEDURE [surfaceNormal: Vector, lightSource: LightSource, albedo: REAL ← 1, omegaAperture: REAL] RETURNS [irradiance: REAL];

A convenience routine which combines CollimatedLambertianRadiance and SiMpleFilmIrradiance.

SpecFilmIrradiance: PROCEDURE [surfaceNormal: Vector, lightSource: LightSource, albedo: REAL ← 1, omegaAperture: REAL] RETURNS [irradiance: REAL];

A convenience routine which combines CollimatedSpecularRadiance and SimpleFilmIrradiance.

END.