Method and apparatus for translating an arc definition into a series of conic curve definitions
View Patent ↗A method for translating an arc definition into a series of conic curve definitions in a form usable by an imager includes first defining a given ellipse. Two intersecting vectors each intersect the ellipse to determine the exact beginning and ending points of the desired arc. The arc is then broken down into a series of sub-arcs no larger than 90 degrees each. The sub-arcs are then represented as conic curve definitions that are usable by an imager to accomplish imaging or clipping against a specified arc.
1. A method of representing an arc as a series of conic curves, the method comprising:
defining an arc;
determining a bounding box;
calculating vector angles for a starting vector and ending vector;
dividing the arc into a plurality of sub-arcs, each sub-arc being defined by a conic curve definition;
calculating a shape parameter for the conic curve definition;
determining coordinates of a control point and a mid point of an arc chord; and
defining a control point segment between the mid point of the arc chord and the control point.
2. The method of claim 1 , wherein each of the sub-arcs is 90 degrees or less.
3. The method of claim 1 , further comprising:
determining a starting point and ending point of each of the plurality of sub-arcs, wherein the plurality of sub-arcs includes at least a first sub-arc and a second sub-arc and further wherein the ending point of the first sub-arc is the starting point of the second sub-arc.
4. The method of claim 1 , further comprising:
calculating the shape parameter based on a ratio of a distance between the mid point of the arc chord and an intersection of the control point segment and the sub-arc, and a length of the control point segment.
5. The method of claim 1 , wherein a direction of the arc is clockwise.
6. The method of claim 1 , wherein a direction of the arc is counter clockwise.
7. The method of claim 1 , further comprising:
transmitting the conic curve definitions to an imager.
8. A computer-readable medium having computer-readable program code embodied therein, the computer-readable program code when executed causing a computer to perform the method of claim 1 .
9. An apparatus for translating an arc definition into a series of conic curve definitions, comprising:
an arc definer, which defines the arc using a bounding box, starting vector and ending vector;
an arc divider, which divides the arc into a plurality of sub-arcs, each sub-arc being defined by a conic curve definition;
a control point determining module, which determines the control point for each sub-arc, based on the intersection point of the two lines which are tangent to the endpoints of the sub-arcs; and
a shape parameter module which calculates a shape parameter, based on the ratio of a distance between the mid point of the arc chord and an intersection of a control point segment and the sub-arc, and a length of the control point segment.
10. The apparatus of claim 9 , wherein the arc divider further determines a starting point and ending point for each sub-arc.
11. The apparatus of claim 9 , further comprising:
an input/output interface which outputs the ending point, control point and shape parameter for each sub-arc to an imager.