Class Name: Arc

Superclass - <Linear Geometry>

Subclasses

Definition

An instance of this DRM class specifies a symmetric curved line, the endpoints of which are specified by the <Base Vertex> components, such that the curve is symmetric about the <Location> component.

Primary Page in DRM Diagram:

• 5

Secondary Pages in DRM Diagram:

Example

1. A geometric representation of a treeline, or a string of lights that follow the path of the <Arc>.

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 centre point, radius, beginning angle, and ending angle. How can I implement this in SEDRIS?

The following formulas show how centre 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 */

               centrex, centrey,    /* centre 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 centre point */
        centrex = -dc;    centrey = -ec;

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

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

Constraints

• <<No Attribute Conflicts>>
• <<Non Crossing Aggregations>>
• <<Non Cyclic Aggregations>>
• <<Precedence of Attribute Set Index>>
• <<Colour Mapping Restrictions>>
• <<Continuous LOD Restrictions>>
• <<Image Mapping Functions and Texture Coordinates>>
• <<Nested Primitive Geometry>>
• <<Linear Geometry Structure>>

Associated with (two-way)(inherited)

• zero or more {ordered} <Geometry Edge> instances through <Edge Directions>

Composed of (two-way)(inherited)

• zero or more {ordered} <Attribute Set Index> instances
• zero or one <Classification Data> instance
• zero or more <Property Table> instances
• zero or more <Property Table Reference> instances
• zero or more <Property Value> instances
• zero or more <Colour> instances
• zero or more {ordered} <Image Mapping Function> instances
• zero or one <Light Rendering Properties> instance
• zero or one <Presentation Domain> instance
• zero or one <Rendering Priority Level> instance
• zero or one <Rendering Properties> instance
• zero or more <Tack Point> instances
• zero or one <Union Of Primitive Geometry> instance (notes)

Composed of (two-way)

• exactly 2 {ordered} <Base Vertex> instances
• one <Location> instance

Composed of (two-way metadata)(inherited)

• zero or one <Time Constraints Data> instance

Component of (two-way)(inherited)

• one or more <Union Of Primitive Geometry> instances

Inherited Field Elements

Notes

Composed of Notes

Union_Of_Primitive_Geometry

 A <Primitive Geometry> contains a <Union Of Primitive Geometry>
 instance as a component only when that <Primitive Geometry>
 can be decomposed into nested <Primitive Geometry>, as (for
 example) a <Polygon> can be decomposed into subfaces.

Fields Notes

count

 A value of zero (0) indicates that the given <Linear Geometry>
 instance is to be rendered as solid.

 Otherwise, the interpretation of the count depends on whether
 a <Light Rendering Properties> component is present for
 the given <Linear Geometry> instance.

 - If a <Light Rendering Properties> component is present, then
   count is the number of evenly spaced light points to be
   rendered along the <Linear Geometry>.

 - If no <Light Rendering Properties> component is present, then
   count is the number of evenly spaced line segments to be
   rendered along the <Linear Geometry>.

suppressLast

 If count is greater than zero, this flag indicates whether the
 last segment / point in the sequence is suppressed or rendered.