Computing the intensity of specularly reflected light

Abstract

The intensity of specularly reflected light from an illuminated object is represented by an algebraic expression including multiplication, addition, and subtraction operations. The algebraic expression is used in an illumination model, where the illumination model describes the color and intensity of light reflected by the illuminated object. Light reflected by the illuminated object is composed of ambient, diffuse, and specular components. The specular terms used in the illumination model are equivalent in functional form to the diffuse terms, thereby accelerating the computation of color vector c defined by the illumination model. A modified algebraic expression representing specularly reflected light from an illuminated object is defined and used in the illumination model, thereby accelerating computation of color vector c.

1 . A method for computing the intensity of specularly reflected light, comprising: 
 representing the intensity of light reflected specularly from an object illuminated by a plurality of light sources by an algebraic expression;    incorporating the algebraic expression into an illumination model for the illumination of the object, the model having specular illumination terms; and    expressing the specular illumination terms of the illumination model in the same functional form as other terms of the illumination model.    
   
   
       2 . The method of  claim 1 , wherein the algebraic expression does not include division or exponentiation operators.  
   
   
       3 . The method of  claim 1 , wherein the plurality of light sources includes extended light sources and point light sources.  
   
   
       4 . The method of  claim 1 , wherein the algebraic expression is S i (n,h i ,n)=1−n+max{n·(nh i ), n−1}, which describes the intensity of light reflected from a point on the object as measured by an observer, the object illuminated by light from an i th  light source, where n is a unit vector normal to the object at the point of reflection, h i  is a unit vector bisecting an angle subtended by a unit vector pointing towards the i th  light source from the point of reflection and a unit vector pointing towards the observer from the point of reflection, and n is a parameter that describes the shininess of the object.  
   
   
       5 . The method of  claim 4 , wherein the illumination model describes the color and intensity of light reflected from the object illuminated by the i th  light source, the reflected light including specular, diffuse, and ambient components.  
   
   
       6 . The method of  claim 5 , wherein the other terms of the illumination model include diffuse illumination terms and ambient terms.  
   
   
       7 . The method of  claim 6 , wherein the specular illumination terms of the illumination model are expressed in the same functional form as the diffuse illumination terms of the illumination model.  
   
   
       8 . The method of  claim 1 , wherein the algebraic expression is Sm i,k (n,h i ,n)=(1−n/k+max{n·(n/k h i ), n/k−l}) k , which describes the intensity of light reflected from a point on the object as measured by an observer, the object illuminated by light from an i th  light source, where n is a unit vector normal to the object at the point of reflection, h i  is a unit vector bisecting an angle subtended by a unit vector pointing towards the i th  light source from the point of reflection and a unit vector pointing towards the observer from the point of reflection, n is a parameter that describes the shininess of the object, and k is a parameter that determines which derivatives of the algebraic expression are continuous.  
   
   
       9 . The method of  claim 8 , wherein 2≦k≦n.  
   
   
       10 . A machine-readable medium comprising instructions for causing the execution of a method for computing the intensity of specularly reflected light, the method comprising: 
 representing the intensity of light reflected specularly from an object illuminated by a plurality of light sources by an algebraic expression;    incorporating the algebraic expression into an illumination model for the illumination of the object, the model having specular illumination terms; and    expressing the specular illumination terms of the illumination model in the same functional form as other terms of the illumination model.    
   
   
       11 . The machine-readable medium of  claim 10 , wherein the algebraic expression does not include division or exponentiation operators.  
   
   
       12 . The machine-readable medium of  claim 10 , wherein the plurality of light sources includes extended light sources and point light sources.  
   
   
       13 . The machine-readable medium of  claim 10 , wherein the algebraic expression is S i (n,h i ,n)=1−n+max{n·(nh 1 ), n−1}, which describes the intensity of light reflected from a point on the object as measured by an observer, the object illuminated by light from an i th  light source, where n is a unit vector normal to the object at the point of reflection, h i  is a unit vector bisecting an angle subtended by a unit vector pointing towards the i th  light source from the point of reflection and a unit vector pointing towards the observer from the point of reflection, and n is a parameter that describes the shininess of the object.  
   
   
       14 . The machine-readable medium of  claim 13 , wherein the illumination model describes the color and intensity of light reflected from the object illuminated by the i th  light source, the reflected light including specular, diffuse, and ambient components.  
   
   
       15 . The machine-readable medium of  claim 14 , wherein the other terms of the illumination model include diffuse illumination terms and ambient terms.  
   
   
       16 . The machine-readable medium of  claim 15 , wherein the specular illumination terms of the illumination model are expressed in the same functional form as the diffuse illumination terms of the illumination model.  
   
   
       17 . The machine-readable medium of  claim 10 , wherein the algebraic expression is SM i,k (n,h i ,n)=(l−n/k+max{n·(n/k h i ), n/k−l}) k , which describes the intensity of light reflected from a point on the object as measured by an observer, the object illuminated by light from an i th  light source, where n is a unit vector normal to the object at the point of reflection, h i  is a unit vector bisecting an angle subtended by a unit vector pointing towards the i th  light source from the point of reflection and a unit vector pointing towards the observer from the point of reflection, n is a parameter that describes the shininess of the object, and k is a parameter that determines which derivatives of the algebraic expression are continuous.  
   
   
       18 . The machine-readable medium of  claim 17 , wherein 2≦k≦n.  
   
   
       19 . A system for computing the illumination of an object by a plurality of light sources, comprising: 
 a memory configured to store game instructions and an illumination model;    a processor configured to execute game instructions and generate rendering instructions;    a vector processor configured to calculate color vectors using the illumination model, the illumination model having specular illumination terms and diffuse illumination terms expressed in the same functional form; and    a graphics processor configured to render the illuminated object in an image using the color vectors according to the rendering instructions.    
   
   
       20 . The system of  claim 19 , wherein for each light source i, an algebraic expression representing the intensity of light reflected specularly from a point on the object and detected by an observer is substituted into the illumination model yielding a specular illumination term for the light source i.  
   
   
       21 . The system of  claim 20 , wherein the algebraic expression does not contain division or exponentiation operators.  
   
   
       22 . The system of  claim 20 , wherein the algebraic expression for light source i is S i (n,h i ,n)=l−n+max{n·(nh i ), n−l}, where n is a unit vector normal to the object at the point of reflection, h i  is a unit vector bisecting an angle subtended by a unit vector pointing towards light source i from the point of reflection and a unit vector pointing towards the observer from the point of reflection, and n is a parameter that describes the shininess of the object.  
   
   
       23 . The system of  claim 22 , wherein the vector processor evaluates vector dot products for the diffuse and specular illumination terms in parallel.  
   
   
       24 . The system of  claim 20 , wherein the algebraic expression for light source i is SM i,k (n,h i ,n)=(l−n/k+max{n·(n/k h i ), n/k−l}) k , where k is a parameter that determines which derivatives of the algebraic expression are continuous, n is a unit vector normal to the object at the point of reflection, h i  is a unit vector bisecting an angle subtended by a unit vector pointing towards light source i from the point of reflection and a unit vector pointing towards the observer from the point of reflection, and n is a parameter that describes the shininess of the object.  
   
   
       25 . The system of  claim 24 , wherein 2≦k≦n.  
   
   
       26 . The system of  claim 25 , wherein the vector processor evaluates vector dot products for the diffuse and specular illumination terms in parallel.  
   
   
       27 . A method for computing the illumination of an object by a plurality of light sources, comprising: 
 storing game instructions and an illumination model in a memory;    executing game instructions and generating rendering instructions;    representing color vectors with the illumination model, the illumination model having specular illumination terms and diffuse illumination terms expressed in the same functional form;    calculating the color vectors by evaluating vector dot products for the specular and diffuse illumination terms in parallel; and    rendering the object in an image using the color vectors according to the rendering instructions.