Class Name: Arc

Superclass - Linear Geometry

Definition

Three locations in space that represent the beginning, mid, and ending points on an Arc. The beginning and ending points are the Vertices, and the mid point is the Location 3D.

Primary Page in DRM Diagram:

• 5

Example

A geometric representation of a treeline, or a string of lights that follow the path of the arc (see Light Source).

FAQs

An Arc can be defined in different ways. Rather than using SEDRIS' method of three points that define the beginning, mid, and ending points on an Arc, I define an Arc with a center point, radius, beginning angle, and ending angle. How can I implement this in SEDRIS?

The following formulas show how center point, radius, beginning and ending angles can be derived from the first set of information (beginning, mid, and ending points on the Arc).

        double x1, y1,              /* beginning point */
               x2, y2,              /* mid point */
               x3, y3,              /* ending point */

               sx1, sx2, sx3,       /* squared x values */
               sy1, sy2, sy3,       /* squared y values */
               ad, D, E, F,         /* determinate values */
               dc, ec, fc,          /* coefficient values */

               centerx, centery,    /* center point of arc */
               r,                   /* radius of arc */
               ab, ae;              /* beginning & ending angles */

        /* get squared values */
        sx1 = x1*x1;   sx2 = x2*x2;   sx3 = x3*x3;
        sy1 = y1*y1;   sy2 = y2*y2;   sy3 = y3*y3;

        /* get 'a' determinate */
        ad = x1*(y2 - y3) - y1*(x2-x3) + x2*y3 - x3*y2;

        /* get 'D' determinate */
        D = (sx1 + sy1)*(y2 - y3) - y1*((sx2 + sy2) - (sx3 + sy3))
            + y3*(sx2 + sy2) - y2*(sx3 + sy3);

        /* get 'E' determinate */
        E = (sx1 + sy1)*(x2 - x3) - x1*((sx2 + sy2) - (sx3 + sy3))
            + x3*(sx2 + sy2) - x2*(sx3 + sy3);

        /* get 'F' determinate */
        F = (sx1 + sy1)*(x2*y3 - x3*y2) -
             x1*(y3*(sx2 + sy2) - y2(sx3 + sy3)) +
             y1*(x3*(sx2 + sy2) - x2*(sx3 + sy3));

        D = -D;            F = -F;

        /* check for colinear point */
        if (ad == 0.0) {
            fprintf(stderr, "ERROR! colinear point\n");
            fflush(stderr);
            exit(-1);
        }

        /* get coefficients */
        dc = D/(2.0*ad);
        ec = E/(2.0*ad);
        fc = F/ad;

        /* get center point */
        centerx = -dc;    centery = -ec;

        /* get radius */
        r = sqrt((dc*dc + ec*ec - fc));

        /* get beginning and ending angles */
        ab = atan2(y1 - centery, x1 - centerx);
        ae = atan2(y3 - centery, x3 - centerx);
    

Constraints

• No Attribute Conflicts
• Non Crossing Aggregations
• Non Cyclic Aggregations
• Precedence of Attribute Set Index
• Color Mapping Restrictions
• Image Mapping Functions and Texture Coordinates
• Nested Primitive Geometry
• Non Nestable Continuous LOD

Composed of (one-way)(inherited)

• optionally, some {ordered} Attribute Set Indices
• optionally, a Classification Data
• optionally, some Property Tables
• optionally, some Property Table References
• optionally, some Property Values
• optionally, some Tack Points
• optionally, some {ordered} Colors
• optionally, a Light Rendering Properties
• optionally, a Rendering Properties
• optionally, some {ordered} Image Mapping Functions
• optionally, a Rendering Priority Level

Composed of (one-way)

• one Location

Composed of (two-way)(inherited)

• optionally, a Union of Primitive Geometry

Composed of (two-way)

• exactly (2) {ordered} Base Vertices

Composed of (one-way metadata)(inherited)

• optionally, a Time Constraints Data

Component of (two-way)(inherited)

• one or more Union of Primitive Geometries

Inherited Field Elements

Notes

Fields Notes

count

 the number of evenly divided segments/points along the
 <Linear Geometry>. The default value of 0 indicates that
 the <Linear Geometry> is solid.

suppressLast

 flag indicating whether the last segment/point is suppressed.