$\newcommand{\deriv}[2][]{\dfrac{\partial #1}{\partial #2}} \newcommand{\tderiv}[2][]{\tfrac{\partial #1}{\partial #2}} \newcommand{\fderiv}[2][]{\dfrac{d #1}{d #2}} \newcommand{\derivII}[3][]{\dfrac{\partial^2 #1}{\partial #2 \partial #3}} \newcommand{\tderivII}[3][]{\tfrac{\partial^2 #1}{\partial #2 \partial #3}} \newcommand{\derivIII}[4][]{\dfrac{\partial^3 #1}{\partial #2 \partial #3 \partial #4}} \newcommand{\tderivIII}[4][]{\tfrac{\partial^3 #1}{\partial #2 \partial #3 \partial #4}} \newcommand{\derivIV}[5][]{\dfrac{\partial^4 #1}{\partial #2 \partial #3 \partial #4 \partial #5}} \newcommand{\half}{\tfrac{1}{2}} % Macro for 1/2 \newcommand{\ud}{\mathrm{d}} \newcommand{\op}{\circ} \newcommand{\dq}{\dot{q}} \newcommand{\ddq}{\ddot{q}} \newcommand{\dt}{\Delta t}$

PointOnPlane - Constraint a point to a plane

The PointOnPlane constraint constraints a point (defined by the origin of a coordinate frame) to lie in a plane (defined by the origin of another coordinate frame and normal vector).

The constraint equation is:

\[h(q) = (p_1 - p_2) \cdot (g_1 \cdot norm)\]

where \(g_1\) and \(p_1\) are the transformation of the frame defining the plane and its origin, \(p_2\) is the point being constrained, and \(norm\) is the normal vector of the plane expressed in the local coordinates of \(g_1\).

By defining two of PointOnPlane constraints with normal plane, you can constrain a point to a line. With three constraints, you can constraint a point to another point.

Examples

pccd.py, pypccd.py, radial.py

class trep.constraints.PointOnPlane(system, plane_frame, plane_normal, point_frame, name=None)

Create a new constraint to force the origin of point_frame to lie in a plane. The plane is coincident with the origin of plane_frame and normal to the vector plane_normal. The normal is expresed in the coordinates of plane_frame.

PointOnPlane.plane_frame

This is the coordinate frame the defines the plane.

(read-only)

PointOnPlane.normal

This is the normal of the plane expressed in plane_frame coordinates.

PointOnPlane.point_frame

This is the coordinate frame that defines the point to be constrained.