Segment Orthogonality

Definition

The SegmentOrthogonality energy ensures that a segment, defined as two point variables ps and pe, is orthogonal to a fixed direction, defined from a unit vector vdir.

Requirements

To use the SegmentOrthogonality energy the following variables must be defined in the solver:

  • ps : Point variable corresponding to the start of the segment.
  • pe : Point variable corresponding to the end of the segment.

The target direction vdir is not add as a variable of the guided projection algorithm*. It is specified at initialisation of the constraint.

Suggestions

No remarks.

Energy Formulation

The formulation of the SegmentOrthogonality energy reads :

Formulation of the SegmentOrthogonality energy

which, in the case where the points are from a three-dimensional space, develops to :

Developed formulation of the SegmentOrthogonality energy

Hence, the local problem can be expressed as follow:

Reduced vector x for the SegmentOrthogonality constraint , Linear part of the SegmentOrthogonality constraint , Constant part of the SegmentOrthogonality constraint

In the framework, the SegmentOrthogonality energy is not restricted to the three-dimensional case. The dimension of the space is given at initialisation of the constraint thanks to the target direction vector vdir.