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System for Defining an Intersection of a Line And a Quadratic Curve

IP.com Disclosure Number: IPCOM000120566D
Original Publication Date: 1991-May-01
Included in the Prior Art Database: 2005-Apr-02
Document File: 3 page(s) / 72K

Publishing Venue

IBM

Related People

Hidaka, K: AUTHOR

Abstract

Disclosed is a system for defining an intersection of a line and a quadratic curve. This system provides a function for selecting a point corresponding to a previously designated intersection point when a line or a quadratic curve, which produces two intersection points, is changed on the display (Figs. 1A-1H).

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System for Defining an Intersection of a Line And a Quadratic Curve

      Disclosed is a system for defining an intersection of a
line and a quadratic curve.  This system provides a function for
selecting a point corresponding to a previously designated
intersection point when a line or a quadratic curve, which produces
two intersection points, is changed on the display (Figs. 1A-1H).

      In computer graphics systems, it is difficult to redraw an
intersection of a line and a quadratic curve, or an object containing
this intersection point. To redraw such graphics objects, the system
needs a function for identifying two intersection points, whose x-y
values are calculated by simultaneous equations (1) and (2).

      The major characteristic of this disclosure is a mechanism for
identifying one of two intersection points by using the inner product
of vectors.  Fig. 2 shows examples of a line and a circle. I1 (X1,
Y1) and I2 (X2,Y2) are solutions of simultaneous equations (3) and
(4).
V1 is a vector defined by P and Q. V2 is another vector defined by
I1 and I2. Each has the direction of P to Q or I1 to I2.
The inner product K of V1 and V2 is calculated from formula (5).
K takes a plus quantity, if the V1 and V2 have the same directions.
K takes a minus quantity, if the V1 and V2 have the opposite
directions.  If K is plus, the system defines the characteristic
value of I1 (T1) as "0," and that of I2 (T2) as "1." If K
is minus, the system defines T1 as "1," a...