ofxMathMesh

ofxMathMesh allows you to create ofMeshs form mathematical equations. You can create meshes from 3dFunctions, 2dFunctions, Parametric Surfaces and Parametric Curves

you can see a small demo here - https://vimeo.com/98150899

Features

• Creates Meshes from 3d Functions, 2d Functions, Parametric Surfaces and Parametric Curves

• Auto Calculates Surface Normals

• Customize Colors and TexCoords on both Front and Back Sides

• Draw wireframe and point meshes with customized color.

• Control bounds and resolution of your mesh

How to Use

Step 1 - create a subclass

you can subclass from anyone of these parents:

• ofx3dFunction - if your equation is of the form y = f(x,z)
• ofx2dFuntion - if your equation is of the form y = f(x)
• ofxParametricSurface - if your equation is of the form r = r(u,v)
• ofxParametrixCurve - if your equation is of the form r = r(t)

For Example to create a Sphere(which is a parametric Surface) you do this:

class Sphere:public ofxParametricSurface

Step 2 - override

in order to customize your mesh you must override one or more of the following functions:

• valueForPoint - mandatory
• colorForPoint - optional
• texCoordForPoint - optional
• backColorForPoint- optional
• backTexCoordForPoint - optional

For example to create a Sphere thats half red half blue you do this:

class Sphere:public ofxParametricSurface {
public:
    ofPoint valueForPoint(float u, float v){
        float x = cos(u) * sin(v);
        float y = sin(u) * sin(v);
        float z = cos(v);
        return ofPoint(x,y,z);
    }
    
     ofFloatColor colorForPoint(float u,float v,ofPoint value){
        if (u > M_PI && u < 2*M_PI - .0001) {
            return ofFloatColor::blue;
        }else{
            return ofFloatColor::red;
        }
    }

};

Step 4 - call setup

setup must be called in order to create a mesh. In setup you specify the bounds and step of your equation. Lower step means higher resolutions. For example to set up a full sphere you do this:

Sphere mySphere;
mySphere.setup(0, 2*M_PI, 0, M_PI, .1, .1);

here u goes form 0 to 2PI, v goes from 0 to PI, and uStep = .1, and vStep = .1. Note that if you want to change the bounds of the equation after setup,you cannot go outside the initial setup bounds.

Step 5 - call draw

to draw your equation you call either draw , drawWireFrame, or drawPoints

    mySphere.draw(true, false);
    mySphere.drawWireFrame(true);
    mySphere.drawPoints(true);

The 1st argument specifies whether you over-rid colorForPoint. The 2nd argument specifies whether you over-rid texCoordForPoint. The results looks like this

Step 6 - reloading

whenever to you update your equation, colors, texcoords,or bounds.You want to call reload()

mySphere.reload()

this is useful for animation and live updates of your equation. If you are reloading constantly its a good idea to call this in the update() function.

Step 7 - drawing two sided

if you want to have different colors and textures on front and backside, you need to implement either backColorForPoint or backTexCoordForPoint. Then call the functions drawFrontFaces and drawBackFaces

For example to draw a sphere that is red and blue on the front and green and yellow on the back, you would do this.

class Sphere:public ofxParametricSurface {
public:
    ofPoint valueForPoint(float u, float v){
        float x = cos(u)* sin(v);
        float y = sin(u)* sin(v);
        float z = cos(v);
        return ofPoint(x,y,z);
    }
    
    ofFloatColor colorForPoint(float u,float v,ofPoint value){
        if (u > M_PI && u < 2*M_PI - .0001) {
            return ofFloatColor::blue;
        }else{
            return ofFloatColor::red;
        }
    }
    
    ofFloatColor backColorForPoint(float u,float v,ofPoint value){
        if (u > M_PI && u < 2*M_PI - .0001) {
            return ofFloatColor::green;
        }else{
            return ofFloatColor::yellow;
        }
    }
};

 	mySphere.setUMax(1.5 *M_PI);
    mySphere.reload();
    mySphere.drawFrontFaces(true, false);
    mySphere.drawBackFaces(true, false);

this is the resulting sphere. Draw part open(uMax set to 1.5PI)

step 8 - getting an ofMesh

You retrieve an ofMesh from your equation by calling getMesh() or getBackMesh

    // returns a mesh which with vertices,frontNormals,frontColors,and frontTexCoords
    ofMesh myMesh = mySphere.getMesh();
    
    // returns a mesh which with vertices,backNormals,backColors,and backTexCoords
    ofMesh myBackMesh = mySphere.getBackMesh();

step 9 - normals

Normals are auto calculated using these formulas, if you want to draw the normals you can use the functions drawNormals(float length) or drawFaceNormals(float length)

Extras

There are a lot more things you can do with this add-on so if you have any questions, you can ask me on the forum thread. Remember Have Fun!