Granted Patent B2

US 6,867,776 · App. 10/042,647 · Granted Mar 15, 2005

Abstract

Claims (23)

1. A method for generating images comprising the steps of:

introducing information into a computer from which the images are produced;

producing the images with texture that do not have visible grid artifacts with the computer using a bit-manipulation to generate a six bit quantity from an integer lattice point i,j,k, where the six bit quantity is defined as a lower six bits of a sum:

b(i,j,k,0)+b(j,k,i,1)+b(k,i,j,2)+b(i,j,k3)+b(j,k,i,4)+b(k,i,j,5)+b(i,j,k,6)+b(j,k,i,7)

define b(i,j,k,B);

patternIndex=4*bit B ( i )+2*bit B ( j )+bit B ( k ) return bitPatterns[patternIndex]

where B is 0 or a positive integer;

generating a gradient direction using the six bit quantity; and

displaying the images on a display.

2. A method for generating images comprising the steps of:

introducing information into a computer from which the images are produced;

producing the images with texture that do not have visible grid artifacts with the computer by placing an input point x,y,z onto a simplicial grid; where x, y and z are integers;

skewing the input point to:

define skew(( x,y,z )−>( x′,y′,z ′)): s=( x+y+z )/3 ( x′,y′,z ′)=( x+s,y+s,z+s ); and

displaying the images on a display.

3. A method as described in claim 2 including the step of using the skewed input point to determine a surrounding unit cube whose corner vertex with lowest coordinate values is:

( i′,j′,k ′)=(floor( x ′),floor( y ′),floor( z ′)).

4. A method as described in claim 3 wherein the producing step includes the step of evaluating each vertex of all 4 vertices of the grid.

5. A method for generating images comprising the steps of:

producing the images with texture that do not have visible grid artifacts with the computer by decomposing a hypercube into n! simplices, where each simplex corresponds to

an ordering of an edge traversal of the hypercube from its lowest vertex (0,0, . . . , 0) to its upper vertex (1,1 . . . , 1), where n is greater than or equal to 3 and is an integer; and

displaying the images on a display.

6. A method as described in claim 5 wherein the producing step has a computational complexity on the order of n 2 .

Assignments (7)