# Tangent to parametric curve
**URL:** https://discourse.processing.org/t/tangent-to-parametric-curve/19788
**Category:** Coding Questions
**Tags:** homework
**Created:** [April 14, 2020, 10:12pm UTC](https://discourse.processing.org/t/tangent-to-parametric-curve/19788 "2020-04-14T22:12:15Z")
**Posts on this page:** 20
**Page:** 1
### Author:  [@mcaaaalvo](https://discourse.processing.org/u/mcaaaalvo)
#### Post date: [April 14, 2020, 10:12pm UTC](https://discourse.processing.org/t/tangent-to-parametric-curve/19788/1 "2020-04-14T22:12:15Z")
I have to create a program, that when I put the mouse on any point of the curve, it draws its tangent line, and writes to me in a corner the value of the slope of this line. The drawing have to include the cartesian axis. The equation and the parameterization are:
BOW CURVE: (x^4)+(y^3)-((x^2)\*y)=0
PARAMETERIZATION: x=t-t^3 and y=t^2-t^4
The code I have right now is this:
```auto
float a=300;
float angle=((-4*pow(mouseX,2)+2*mouseX*mouseY)/((3*pow(mouseY,2)-pow(mouseX,2))));
float w=300;
void setup(){
size(750,750);
}
void draw(){
background(255);
//AXIS(height,width);
translate(width/2,height/2);
for(float t=0; t<2*PI; t=t+0.001){
stroke(255,128,0);
strokeWeight(1.25);
point(a*(t-pow(t,3)),-a*(pow(t,2)-pow(t,4)));
point(-a*(t-pow(t,3)),-a*(pow(t,2)-pow(t,4)));
}
{
angle=atan(((-4*pow(mouseX,2)+2*mouseX*mouseY)/((3*pow(mouseY,2)-pow(mouseX,2)))));
pushMatrix();
translate(mouseX-width/2,mouseY-height/2);
rotate(((-4*pow(mouseX,2)+2*mouseX*mouseY)/((3*pow(mouseY,2)-pow(mouseX,2)))));
line(-w,0,w,0);
popMatrix();
}
}
```
There is something wrong with the code, if anyone could help me please.
The implicit derivative of the curve is this:
---
### Author:  [@Chrisir](https://discourse.processing.org/u/Chrisir)
#### Post date: [April 14, 2020, 10:34pm UTC](https://discourse.processing.org/t/tangent-to-parametric-curve/19788/2 "2020-04-14T22:34:01Z")
Please hit ctrl-t in processing prior to posting
When posting mark your code as code using \<\> Symbol in the command bar of the forum
---
### Author:  [@mcaaaalvo](https://discourse.processing.org/u/mcaaaalvo)
#### Post date: [April 14, 2020, 10:41pm UTC](https://discourse.processing.org/t/tangent-to-parametric-curve/19788/3 "2020-04-14T22:41:59Z")
Idon’t know how to do it, could you help me with my code??
---
### Author:  [@Chrisir](https://discourse.processing.org/u/Chrisir)
#### Post date: [April 15, 2020, 8:32am UTC](https://discourse.processing.org/t/tangent-to-parametric-curve/19788/4 "2020-04-15T08:32:43Z")
> [@mcaaaalvo](#):
>
> PARAMETERIZATION
what is this exactly?
---
### Author:  [@mcaaaalvo](https://discourse.processing.org/u/mcaaaalvo)
#### Post date: [April 15, 2020, 8:43am UTC](https://discourse.processing.org/t/tangent-to-parametric-curve/19788/5 "2020-04-15T08:43:55Z")
Make a function dependin on x and y, which they depend on t
Do you know how to fix it??
---
### Author:  [@Chrisir](https://discourse.processing.org/u/Chrisir)
#### Post date: [April 15, 2020, 9:16am UTC](https://discourse.processing.org/t/tangent-to-parametric-curve/19788/6 "2020-04-15T09:16:32Z")
> [@mcaaaalvo](#):
>
> when I put the mouse on any point of the curve, it draws its tangent line, and writes to me in a corner the value of the slope of this line.
when you mean the slope of this line, it’s rather the slope **of the section** of this line, right?
Or is it the same everywhere?
So the function must know where the mouse is on the graph?
maybe I can help you later
---
### Author:  [@Chrisir](https://discourse.processing.org/u/Chrisir)
#### Post date: [April 15, 2020, 9:26am UTC](https://discourse.processing.org/t/tangent-to-parametric-curve/19788/7 "2020-04-15T09:26:57Z")
> [@mcaaaalvo](#):
>
> implicit derivative
what is this exactly? The slope?
---
### Author:  [@Chrisir](https://discourse.processing.org/u/Chrisir)
#### Post date: [April 15, 2020, 9:28am UTC](https://discourse.processing.org/t/tangent-to-parametric-curve/19788/8 "2020-04-15T09:28:00Z")
> [@mcaaaalvo](#):
>
> There is something wrong with the code
what is wrong exactly?
---
### Author:  [@mcaaaalvo](https://discourse.processing.org/u/mcaaaalvo)
#### Post date: [April 15, 2020, 9:28am UTC](https://discourse.processing.org/t/tangent-to-parametric-curve/19788/9 "2020-04-15T09:28:45Z")
I think the slope is the same everywhere.
Yes please, hahah i have to hand on the homework before the April 18, And I have to fix that problem hahaha
Thanks!!!
---
### Author:  [@Chrisir](https://discourse.processing.org/u/Chrisir)
#### Post date: [April 15, 2020, 9:30am UTC](https://discourse.processing.org/t/tangent-to-parametric-curve/19788/10 "2020-04-15T09:30:43Z")
**Parametrization** , also spelled **parameterization** , **parametrisation** or **parameterisation** , is the process of defining or choosing [parameters](https://en.wikipedia.org/wiki/Parameter).
> **[Parametrization](https://en.wikipedia.org/wiki/Parametrization)**
>
> Parametrization, also spelled
> parameterization,
> parametrisation or
> parameterisation,
> is the process of defining or choosing parameters.
> Parametrization may refer more specifically to:
> Parameter (disambiguation)
> .mw-parser-output table.dmbox{clear:both;margin:0.9em 1em;border-top:1px solid #ccc;border-bottom:1px solid #ccc;background-color:transparent}
---
### Author:  [@Chrisir](https://discourse.processing.org/u/Chrisir)
#### Post date: [April 15, 2020, 9:32am UTC](https://discourse.processing.org/t/tangent-to-parametric-curve/19788/11 "2020-04-15T09:32:52Z")
> [@Chrisir](#):
>
> > [@mcaaaalvo](#):
> >
> > implicit derivative
>
> what is this exactly? The slope?
can you please answer this?
---
### Author:  [@Chrisir](https://discourse.processing.org/u/Chrisir)
#### Post date: [April 15, 2020, 9:34am UTC](https://discourse.processing.org/t/tangent-to-parametric-curve/19788/12 "2020-04-15T09:34:44Z")
> [@mcaaaalvo](#):
>
> I think the slope is the same everywhere.
I really don’t think so …
😉
> [@Chrisir](#):
>
> what is wrong exactly?
what is wrong exactly?
---
### Author:  [@mcaaaalvo](https://discourse.processing.org/u/mcaaaalvo)
#### Post date: [April 15, 2020, 9:44am UTC](https://discourse.processing.org/t/tangent-to-parametric-curve/19788/13 "2020-04-15T09:44:38Z")
thw implicit derivative is just the derivative of the function, and what is wrong is that the tangent line doesn’t fit with the drawing
---
### Author:  [@mcaaaalvo](https://discourse.processing.org/u/mcaaaalvo)
#### Post date: [April 15, 2020, 9:58am UTC](https://discourse.processing.org/t/tangent-to-parametric-curve/19788/14 "2020-04-15T09:58:37Z")
Maybe that haha 
---
### Author:  [@Chrisir](https://discourse.processing.org/u/Chrisir)
#### Post date: [April 15, 2020, 10:29am UTC](https://discourse.processing.org/t/tangent-to-parametric-curve/19788/15 "2020-04-15T10:29:55Z")
At the moment, we see the slope throughout from the mouse. I don’t like it.
Are you into OOP?
If I were you I made a class PointOfGraph which stores the points and also the
implicit derivative/ slope for this point.
Fill it in setup() with this:
```auto
for (float t=0; t<2*PI; t=t+0.001) {
stroke(255, 128, 0);
strokeWeight(1.25);
point(a*(t-pow(t, 3)), -a*(pow(t, 2)-pow(t, 4)));
point(-a*(t-pow(t, 3)), -a*(pow(t, 2)-pow(t, 4)));
}
```
Display it in draw():
Now, check if mouse is on a point and then display the slope.
Below is another idea, an example that displays slope tangent line only when the mouse is on a point of a graph. It doesn’t work. When the implicit derivative of the curve is correct in your code, maybe the usage of atan is wrong?
I can’t help you no more.
Chrisir
```auto
float a=300;
float angle=0; // =((-4*pow(mouseX, 2)+2*mouseX*mouseY)/((3*pow(mouseY, 2)-pow(mouseX, 2))));
float w=300;
void setup() {
size(750, 750);
}
void draw() {
//
background(255);
//AXIS(height,width);
translate(width/2, height/2);
for (float t=0; t<2*PI; t=t+0.001) {
stroke(255, 128, 0);
strokeWeight(1.25);
point(a*(t-pow(t, 3)), -a*(pow(t, 2)-pow(t, 4)));
point(-a*(t-pow(t, 3)), -a*(pow(t, 2)-pow(t, 4)));
// only for THE FIRST POINT !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
if (dist(mouseX-width/2, mouseY-height/2,
a*(t-pow(t, 3)), -a*(pow(t, 2)-pow(t, 4)) ) < 8)
{
angle=atan(((-4*pow((mouseX-width/2), 2)+2*(mouseX-width/2)*(mouseY-height/2))
/
((3*pow((mouseY-height/2), 2)-pow((mouseX-width/2), 2)))));
pushMatrix();
translate(mouseX-width/2, mouseY-height/2);
rotate(angle);
line(-w, 0,
w, 0);
popMatrix();
}
}//for
}
```
---
### Author:  [@quark](https://discourse.processing.org/u/quark)
#### Post date: [April 15, 2020, 10:51am UTC](https://discourse.processing.org/t/tangent-to-parametric-curve/19788/16 "2020-04-15T10:51:46Z")
Is this what you hope to achieve 😄
[ ](https://www.youtube.com/watch?v=McB7iK3o-tI)
---
### Author:  [@mcaaaalvo](https://discourse.processing.org/u/mcaaaalvo)
#### Post date: [April 15, 2020, 5:35pm UTC](https://discourse.processing.org/t/tangent-to-parametric-curve/19788/17 "2020-04-15T17:35:58Z")
Thank you so much for your work, don’t worry, i’ll continue trying new things basing on he code you fixed.
Thank you so much
---
### Author:  [@quark](https://discourse.processing.org/u/quark)
#### Post date: [April 15, 2020, 5:45pm UTC](https://discourse.processing.org/t/tangent-to-parametric-curve/19788/18 "2020-04-15T17:45:33Z")
I don’t understand - I have not provided any other code related to this discussion on tangents. I simply posted the video to confirm what is expected so I don’t waste time explaining the wrong solution.
---
### Author:  [@mcaaaalvo](https://discourse.processing.org/u/mcaaaalvo)
#### Post date: [April 15, 2020, 5:46pm UTC](https://discourse.processing.org/t/tangent-to-parametric-curve/19788/19 "2020-04-15T17:46:06Z")
And you could fix my code? or telling me what’s wrong?
---
### Author:  [@quark](https://discourse.processing.org/u/quark)
#### Post date: [April 15, 2020, 5:52pm UTC](https://discourse.processing.org/t/tangent-to-parametric-curve/19788/20 "2020-04-15T17:52:51Z")
I can _explain_ what you need to do to make behave like the video. I will not provide the actual code since it is homework.
Do you want me to do that???
[Next page](https://discourse.processing.org/t/tangent-to-parametric-curve/19788.md?page=2)