# Theoretical math question

**URL:** <https://forum.kirupa.com/t/theoretical-math-question/193886>\
**Category:** random\
**Created:** [July 19, 2006, 1:38am UTC](https://forum.kirupa.com/t/theoretical-math-question/193886 "2006-07-19T01:38:33Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![MTsoul](https://avatars.discourse-cdn.com/v4/letter/m/91b2a8/32.png) [@MTsoul](https://forum.kirupa.com/u/MTsoul)\
**Post date:** [July 19, 2006, 1:38am UTC](https://forum.kirupa.com/t/theoretical-math-question/193886/1 "2006-07-19T01:38:33Z")

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This is somewhat related to Actionscript, but not really, so I put it in Random.

Given a parametric curve in 2D (3D later), **r** (t) = [u(t), v(t)] a vector dependent on the variable **t** , how would it be possible to plot it?

**1.** The most obvious one would be point by point. Select a t and graph a point at the corresponding coordinate, then connect it to the next point.

This seems rather dumb doesn’t it? It’s like guess and check, for a plot. It also takes a (relatively) long time for complex equations.

**2.** Since Actionscript supports the .moveTo() function, I think that’ll work better. If you don’t know it, it has 4 parameters: x and y of the next point, and x and y of a control point. The control point is the intersection point of the tangents of the current point and the next point.

But mathematically speaking, how is it possible to translate a parametric curve to that format? The only way I can think of is still taking points on the curve, find their tangents/intersections, and connect them. That’ll require fewer points for the same precision, but it still doesn’t seem systematic.

**Simple example** :

Plot r(t) = [t^2, 1-t] with {0 \<= t \<= 5}

Seems like I’d still have to take a few points, say t = 0, 1, 2, 3, 4, and 5, then get each corresponding (x,y) value and graph it. Is there no other way?