the tangent is the difference between point 0 and point 1.

you're using it as an absolute value, drawing from point 0 (200, 0, 0) to (-.999, 19, 0). it's all there in your debug.

you need to multiply the tangent value by some largish number (or you'll never see it) and then draw from p0 to (p0 + multiplied tangent). and change the stroke colour before you do this so you can see it.

> Vec3D is my class that extends PVector, but for now it does nothing.

then why bother? all you've done is make it hard for people to help you debug your code.

hei!

The code you use to calculate the points on a circle actually go round the circle nearly 3 times! In you code you have

1.  float theta = 0;
2.   for (int i=0; i<100; i++) {
3.     float x = cos(theta)*200;
4.     float y = sin(theta)*200;
5.     float z = 0;
6.     theta += 0.1;
7.     
8.     points[i] = new Vec3D(x,y,z);
9.   }

Therefore theta the angle goes from 0 to 10 radians when it should be 0 to 2 Pi. This is clearer if you change line 5 to
float z = i * 1.1;

To correct this change line 6 to
theta += TWO_PI / 99;

Notice that I have divided by 99 rather than 100 this is so that the two ends meet to make a complete circle.

the tangent drawn is a line that go in 0,0,0.

since your circle is centred about 0,0,0 then it would be a radius not a tangent.

the tangent is the difference between point 0 and point 1.

since point 0 and point 1 represent adjacent points on the circumference this can be used to calculate an approximation to the tangent. The smaller the angular distance between the points the more accurate the result, but it is still an approximation. In this case it is probably close enough but could be well out for more complicated/curvacious shapes.

actually i'm going to find frame composed by tangent binormal an normal for finding local coordinate system  to extrude curve in a tubolar surface, like a tube. 

The tangent to a circle is a simple vector but when you consider the tangent to a point on the curved surface of a tube it becomes a plane. To make this clearer consider this. If you place a cylinder so that its curved surface is touching the surface of a flat table, then the table surface (plane) is the tangent to any point of contact between the cylinder and table i.e. any straight line drawn on the table top to the point of contact is a tangent.

As to the Vec3D class extending the PVector class

first of all, i'm going to implement myself some method like rotation around axes and others.

not implemented yet.

I would recommend creating a class to represent rotations and this class would have methods to manipulate vectors e.g. rotate about a given axis etc. This is a much better aproach and the one used in the Apache Commons Mathematics project.
This library has a Rotation class and its own Vector3D class which you might use rather than create your own. Alternatively the Shapes3D library has a Rot class which is a version of the Rotation class but works with the PVector class. The source code for the Shapes3D library might be a place to see some simple 3D shape coding.

Best of luck with your project.

hei guys!

Could not run the code you posted the Vec3D class needed a constructor i.e.

1. class Vec3D extends PVector { /* TODO */
2.   public Vec3D(float x, float y, float z) {
3.     super(x,y,z);
4.   }
5. }

Once I did this it worked and looked very pretty.

actually, shape3d libs is what inspired my project, but i don't want to make a library, i tried to read the code of shape3d but it's quite hard for me till now.. are you involved in that?

I created the Shapes3D library so I am glad I managed to inspire someone to do something challenging.

ahah ohy yeah, thanks for explanation, really clear (it's really difficult to find good explanation of math concepts that not involeved bad and big formulas).

Unfortunately 2D and 3D graphics programming involves a lot of maths. I had not heard of the parallel transport method so I googled it - sounds neat but again involves some heavy maths.

With regard to Bezier curves Processing has some methods for working with them. This link shows how to calculate the tangent and normals in 2D. In 2D both the tangent and normal is a simple vector. In 3D the tangent is a simple vector but there are an infinite number of normals for any point on the curve. This caused me some headackes when I developed the BezTube shape for the library.

(ohu, yeah, i didn't past all Vec3D)