Previous Up Next

11.18.1  Loci: locus

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 this, the locus command takes two mandatory arguments and two optional arguments.

locus will draw the locus of points formed by the first argument, as the second argument traces over the curve C.
Input:

P := element(line(i, i+1))

then:

G := isobarycenter(-1,1,P)

then:

locus(G,P)

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.
Output:

Input:

parameq(C)

Output:

t + i

Input:

locus(G,P,t=-3..3,tstep=0.1)

Output:

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

For this, the locus command takes two mandatory arguments and two optional arguments.

locus will draw the envelope of the lines formed by the first argument, as the second argument traces over the curve C.
Input:

F := point(1)

then:

H := element(line(x=0))

then:

d := perpen_bisector(F,H)

then:

locus(d,H)

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. Output:

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.
Input:

H := element(line(y=0))

then:

D := line(y + x*tan(affix(H)) - 2*sin(affix(H)))

then:

locus(D,H)

Output:

Input:

locus(D,H,t=0..pi)

Output:


Previous Up Next