Method and apparatus for rendering volumetric images

A method for drawing a single pixel antialiased line by rendering two pixels nearest an ideal line having a start point and an end point on a display of a computer having a memory for storing a color value for a pixel before outputting the color value to the display, comprising the steps of:

• (a) determining a subrod of voxels corresponding to each pixel in the line from a rod of voxels;
• (b) determining the color value for each pixel based on a voxel color value and a voxel opacity coefficient corresponding to each voxel in the subrod of voxels corresponding to each pixel;
• (c) calculating a first absolute value of a difference between a first coordinate of the start point and a first coordinate of the end point;
• (d) determining coordinates for a first pixel closest to an idealized line between the start point and the end point;
• (e) calculating a Bresenham error term for said first pixel;
• (f) calculating a vertical distance between the idealized line and a position of a pixel below the idealized line;
• (g) calculating a Sfarti error term representing a product between the vertical distance and the first absolute value;
• (h) determining coordinates for a second pixel adjacent to said first pixel closest as a function of the sign of said Sfarti error term, said first pixel and said second pixel forming a pair of pixels straddling the idealized line;
• (i) determining a first coverage for the first pixel as a function of a value of a distance between the idealized line and the first pixel, said coverage pixel being determined using fractional components of coordinates, wherein said coordinates are represented with fixed point numbers;
• (j) determining a second coverage for the second pixel as a function of a value of a distance between the idealized line and the second pixel, said coverage pixel also being determined using fractional components of coordinates;
• (k) determining an intensity value for the pair of pixels as a function of the first coverage and the second coverage;
• (l) writing color values into the memory for said pair of pixels based on the intensity of the pair of pixels, said pixel color value representing both hue and brightness;
• (m) outputting the color values for said pair of pixels to the display;
• and
• (n) incrementing said Bresenham error term by a first predetermined value;
• (o) incrementing said vertical distance by a second predetermined value;
• (p) incrementing said Sfarti error term by a third predetermined value;
• (q) incrementing a first coordinate of said first pixel by a fourth predetermined value and incrementing a second coordinate of said first pixel by a fifth predetermined value, said fourth and fifth predetermined values being a function of said Bresenham error term;
• (r) repeating steps (h) through (q) until color values for a pair of pixels closest to the end point have been output in step (m).

A method for rendering a three dimensional graphic object in a two dimensional display space, comprising the steps of:

• segmenting the object into a plurality of parallelepipeds;
• decomposing each of the parallelepipeds into at least one rod of voxels, said rod of voxels being determined based upon sampling at least two pixels for each actual ideal pixel and determining pixel coverage using fractional components of fixed point pixel coordinates, with each of the rods of voxels being parallel to a depth axis of the display space;
• and
• projecting the rods of voxels onto an X-Y plane of the display space as lines of pixels.

A method for drawing a single pixel antialiased line by rendering two pixels nearest an ideal line, said method comprising the steps of:

• selecting pairs of adjacent pixels straddling the ideal line;
• determining intensity and color values for said pixels using fractional components of coordinates, wherein said coordinates are represented with fixed point numbers, said color and intensity values of said two pixels being selected to give the appearance of only a single pixel for each pair of pixels when displayed;
• and
• rendering a line by displaying a plurality of said pairs of pixels along the ideal line.