A point proportion t along a curve is defined variously for different types of curves as follows:
- For a Line segment AB, it defines the point (1-t)*A + t*B
- For a Circle it defines the point on the circle which subtends angle t at the center.
- For a Locus or envelope, it defines the point at parameter value t.
- For general Cartesian functions, it defines the x value of the point on the function.
- For Polar functions, it defines the point on the function which subtends angle t.
- For general Parametric functions, it defines the point at parameter value t.
- For an Ellipse of the form X2/a2 + Y2/b2 =1 it defines the point (a cos(t), b sin(t)).
- For a Parabola of the form Y=X2/4a it defines the point (2at, at2)
- For a Hyperbola of the form X2/a2 - Y2/b2 =1 it defines the point (a/cos(t), (b sin(t))/cos(t)).
- Select
a point and one of the curves mentioned above. - Click the Point Proportional icon
from the Constrain toolbox, or select Point Proportional from the Constrain menu. - Enter the parameter or quantity in the data entry box.
For example, in the following diagram, D is defined proportion t along AB, and E is defined proportion t along BC. The curve is the locus of F as t varies between 0 and 1.
In the following example, the curve Y=X2 . Tangents are created at points with parameter values x0 and x1 on this curve. Point C is calculated for the current location of the tangents.
