Regularized tangents in computer graphics
AssigneeAutodesk, Inc.
InventorKenneth Jamieson Hill
Life of this patent
Estimating the term…
Abstract
A method, apparatus and article of manufacture for generating regularized tangents of curves. The method comprises the steps of bounding a length of the arc, computing a chord vector, where the chord vector corresponds to the bounded length of the arc, generating a tangent vector, where the tangent vector is substantially normal to the chord vector, and regularizing the tangent vector, where the regularized tangent vector approximates a true tangent vector to the arc.
Claims25
A method for generating a tangent to an arc in an output media of a computer, comprising the steps of:
- (a) obtaining two or more points to be utilized to define an arbitrary curve;
- (b) producing a spline that passes through the two or more points;
- (c) selecting one of the points in the curve;
- (d) generating a tangent vector at the selected point that defines a direction and magnitude for an arc passing through the selected point
- (e) computing a scaling factor based on an estimated arc length of the arc;
- (f) converting the tangent vector into a derivative for use in constructing the arc using the scaling factor;
- and
- (g) drawing the tangent to the arc on the output media of the computer.
An apparatus for generating a tangent to an arc for display on a computer, the apparatus comprising:
- (a) a computer;
- (b) means, performed by the computer, for obtaining two or more points to be utilized to define an arbitrary curve;
- (c) means, performed by the computer, for producing a spline that passes through the two or more points;
- (d) means, performed by the computer, for selecting one of the points in the curve;
- (e) means, performed by the computer, for generating a tangent vector at the selected point that defines a direction and magnitude for an arc passing through the selected point;
- (f) means, performed by the computer, for computing a scaling factor based on an estimated arc length of the arc;
- (g) means, performed by the computer, for converting the tangent vector into a derivative for use in constructing the arc using the scaling factor;
- and
- (h) means, performed by the computer, for drawing the tangent to the arc on an output media of the computer.
A program storage device, readable by a computer, tangibly embodying one or more programs of instructions executable by the computer to perform method steps of generating a tangent to an arc for display on a computer, comprising the steps of:
- (a) obtaining two or more points to be utilized to define an arbitrary curve;
- (b) producing a spline that passes through the two or more points;
- (c) selecting one of the points in the curve;
- (d) generating a tangent vector at the selected point that defines a direction and magnitude for an arc passing through the selected point
- (e) computing a scaling factor based on an estimated arc length of the arc;
- (f) converting the tangent vector into a derivative for use in constructing the arc using the scaling factor;
- and
- (g) drawing the tangent to the arc on the output media of the computer.
Dependencies are inferred from the claim text.