Definition

For a <Linear Geometry> instance G, the following conditions shall hold.

1. Each <Vertex> component of G shall appear exactly once as a component of G.

2. No two <Vertex> components of G shall occupy the same position in space.

3. If G is an <Arc> instance, the <Location> component of G shall not occupy the same position in space as any of the <Vertex> components of G.

4. Let L be a <Linear Geometry> instance that is associated with n ordered <Geometry Edge> instances E₁, ..., E_n through the use of n <Edge Direction> link objects D₁, ..., D_n, where n ≥ 1.

   1. If D₁ has a forwards field value of SE_TRUE, the start <Geometry Node> instance of E₁ shall be associated with the first <Vertex> component of L. Otherwise, the end <Geometry Node> instance of E₁ shall be associated with the first <Vertex> component of L.

   2. If D_n has a forwards field value of SE_TRUE, the end <Geometry Node> instance of E_n shall be associated with the last <Vertex> component of L. Otherwise, the start <Geometry Node> instance of E_n shall be associated with the last <Vertex> component of L.

   3. If n > 1, for each E_i, E_i+1, where i = 1, ..., n-1, E_i and E_i+1 shall associate to a common <Geometry Node> instance. For each consecutive <Geometry Edge> instance E_i within the sequence, D_i shall be consistent with the starting and ending nodes of the edge.

      1. Consider the case where L is a <Line> instance. L shall have exactly n+1 <Vertex> components V_i, each of which has an associated <Geometry Node> instance G_i, which shall be the common <Geometry Node> instance for E_i and E_i+1.

      2. Consider the case where L is an <Arc> instance expressed by a sequence of edges.The <Geometry Node> instances forming the ends of the edges shall all be intersected by the circle for which the <Arc> instance is specifying a subsection.

Rationale

The <Location> information of a <Linear Geometry> instance is required to be distinct in order to form geometrically valid <Linear Geometry> instance.

Example

1. An <Arc> instance, in order to specify a geometric arc, is required to have distinct endpoints, and the <Location> instance about which it is symmetric is required to be distinct from those endpoints for the same reason.

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