Constraints and dimensions

sk.Constrain(a, b, kind, value, id=...) adds a constraint between one or two references, read from a to b: Constrain("line", "circle", px.Tangent) makes the line tangent to the circle. A reference can be

• an element by its id, such as "bottom";

• a point of an element, such as "bottom.start", "bottom.end", "bottom.mid" or "fillet.center";

• a point made with Vertex;

• the sketch’s axes px.H and px.V, or its origin sk.origin.

The geometric kinds also work as flags of the drawing calls (see Drawing with constraints). The dimensions take a value and usually an id, so that they can be changed later.

Kind	Between	Meaning
Coincident	A point and a point, line, circle or spline	The point lies on the other reference
Horizontal, Vertical	A line, or two points	Along px.H or px.V
Parallel, Perpendicular	Two lines	Parallel, or at a right angle
Tangent	Two of line, arc, circle and spline	Touching, on the side as drawn
Equal	Two lines, or two circles and arcs	Equal lengths or radii
Symmetric	Two points and a line	Mirror images of each other
SymmetricCarriers	Two elements and a line	The mirror image of one element’s line or circle is the other’s
Concentric	Two circles or arcs	One common center
Fix	A point or an element	Stays where it is
Distance	A line’s length, or points and lines	A dimension
Radius, Diameter	A circle or arc	A dimension
Angle	Two lines, or a line and an axis	A dimension in degrees
RigidGroup	Elements	Keep their shape and move as one

import planex as px

A plate with a hole, all constraints shown

The example is the plate from the section overview, with a hole of diameter 10, 15 from the bottom and 20 from the left side. show_constraints places a sign next to every constraint: a circle at a coincidence, a square in a perpendicular corner, H and V, two short strokes along a tangent, an anchor for a fixed point, and the value of each dimension with its id (Figure 1a). show_ends marks the start of every line and arc in blue and its end in orange, which is what .start and .end refer to, and show_direction adds arrows (Figure 1b). sk.Plot(show_constraints=True) draws the same with matplotlib. With backend="plotly", the picture is interactive, and every sign is explained on hover.

sk = px.Sketch(id="plate")
sk.Move(sk.origin, px.Coincident)
sk.Line(37, 2.5, px.Horizontal, id="bottom")
sk.Arc(9, 95, px.Tangent, id="fillet")
sk.Line(-1, 17, px.Vertical, px.Tangent, id="right")
sk.Line(-46, 3, px.Perpendicular, id="top")
sk.Close(px.Perpendicular, id="left")
sk.Constrain("fillet", px.Radius, 10, id="r")
sk.Constrain("bottom.start", "right", px.Distance, 50, id="width")
sk.Constrain("bottom", "top", px.Distance, 30, id="height")

sk.Circle(20, 15, 5, id="hole")
sk.Constrain("hole", px.Diameter, 10, id="d")
sk.Constrain("hole.center", "bottom", px.Distance, 15, id="y_hole")
sk.Constrain("hole.center", "left", px.Distance, 20, id="x_hole")
print(sk.status, sk.dof, sorted(sk.dimensions))

full 0 ['d', 'height', 'r', 'width', 'x_hole', 'y_hole']

(a) show_constraints

(b) show_ends and show_direction

Figure 1: A plate with a hole and all its constraints

Reference dimensions

A dimension with reference=True and no value drives nothing; it only measures. sk["diagonal"] is the distance from the plate’s origin to the hole’s center in the current solution, and it follows every change.

sk.Constrain(sk.origin, "hole.center", px.Distance, id="diagonal", reference=True)
print("diagonal", sk["diagonal"], "exact", (20**2 + 15**2) ** 0.5)
sk.Update({"x_hole": 30, "y_hole": 10})
print("diagonal", sk["diagonal"], "exact", (30**2 + 10**2) ** 0.5, sk.status)

diagonal 25.0 exact 25.0
diagonal 31.622776601683793 exact 31.622776601683793 full

Removing a constraint

Remove(id) removes a constraint, and the element it held can move again. Without the hole’s diameter, the sketch has one degree of freedom left.

sk.Remove("d")
print("without d:", sk.status, sk.dof, "degree of freedom")
sk.Constrain("hole", px.Radius, 5, id="d")
print("with d again:", sk.status, sk.dof, "degrees of freedom")

without d: under 1 degree of freedom
with d again: full 0 degrees of freedom