26.17.1  Loci

The locus command draws the locus of points determined by geometric objects moving in the plane, where the object depends on a point moving along a curve. It can draw a locus of points which depends on points on a curve, or the envelope of a family of lines depending on points on a curve.

The locus of points depending on points on a curve.

• For drawing the locus of points depending on points on a curve, locus takes two mandatory arguments and two optional arguments:
  • var₁, a variable name which has already been assigned to a point, which itself is a function of var₂, the second argument.
  • var₂, a variable name assigned to element(C) for some curve C (see Section 26.5.15).
  • Optionally, t=a..b, where t is the parameter of the curve C. (You can double check the name of the parameter for a curve C with the command parameq(C).)
  • Optionally, tstep=s, to set the step size for the parameter t.
• locus(var₁,var₂ ⟨,tstep=c ⟩) draws the locus of points formed by var₁, as var₂ traces over the curve C.

  With the optional arguments, C is limited to the part parameterized from a to b with step size c.

Example

This will draw the set of isobarycenters of the triangles with vertices -1, 1 and P, where P ranges over the line through i and i+1.

The envelope of a family of lines which depend on points on a curve.

For drawing the envelope of a family of lines which depend on points on a curve:

• locus takes two mandatory arguments and two optional arguments.
  • var₁, a variable name which has already been assigned to a line, which itself is a function of var₂, the second argument.
  • var₂, a variable name which has already been assigned to element(C) for some curve C (see Section 26.5.15).
  • Optionally, t=a..b, where t is the parameter of the curve C. (You can double check the name of the parameter for a curve C with the command parameq(C).)
  • Optionally, tstep=s, to set the step size for the parameter t.
• locus(var₁,var₂ ⟨,tstep=c ⟩) draws the envelope of lines formed by var₁, as var₂ traces over the curve C.

  With the optional arguments, C is limited to the part parameterized from a to b with step size c.

Examples

This will draw the envelope of the family of perpendicular bisectors of the segments from the point 1 to the points on the line x=0.

To draw the envelope of a family of lines which depend on a parameter, such as the lines given by the equations y+x tan(t)−2sin(t)=0 over the parameter t, the parameter can be regarded as the affixes of points on the line y=0.