26.5.15 A point on a geometric object in the plane
The element
command is most useful in a 2D
geometry screen; it creates objects that are restricted to a geometric
figure.
element takes different types of arguments.
-
element can take one mandatory argument and one
optional argument:
-
a..b, a range of values.
- Optionally, init and step, an initial
value (by default (a+b)/2) and step size (by default (b−a)/100).
- element(a..b ⟨,init,step ⟩)
creates a parameter restricted to the interval from a to b, with the given
initial value and whose value can be changed in the given step
sizes.
For example, the command t:=element(0..pi) creates a
parameter t which can take on values between 0 and π
and has initial value π/2. It also creates a slider labeled
t which can be used to change the values. The values of
any later formulas involving t will change with t.
-
element can take one mandatory argument and one
optional argument:
-
C, a curve.
- Optionally, init, an initial value (by default
1/2).
- element(C ⟨,init ⟩)
creates a point which will be restricted to the curve, the
initial position of the point is determined by setting the parameter
(in the default parameterization of the object) to the initial
value. If the point can be moved by the mouse (as it can when the
geometry screen is in Pointer mode), then the motion will
be restricted to the geometric object.
For example, the command A:=element(circle(0,2)) creates a
point labeled A whose position is restricted to the circle
of radius 2 centered at the origin. Since the circle has default
parameterization 2 ei t, A starts out at
2 ei/2.
-
element can take two mandatory arguments:
-
P, a polygon or polygonal line with n sides.
- [floor(t),frac(t)], where t is a variable previously
defined by t=element(0..n).
- element(P,[floor(t),frac(t)])
creates a point restricted to the polygonal line. With the
sides numbered starting at 0, the value of floor(t)
determines which side the point is on, and the value of
frac(t) determines how far along the side the point is.