Because Mathematics can be so fun!
K3DSurf is a program to visualize and manipulate Mathematical models in three, four, five and six dimensions. K3DSurf supports Parametric equations and Isosurfaces.
Because an image is worth 1000 words... (*)
And because (*) isn't totally true...
Features
- Interactive visualization with mouse events (Right: Rotate, Middle: translate and left: Scale).
- Real time animation (rotation) and morph (by the introduction of t_time variable). Animation and morph can also be monitored by controls that affect the CPU usage and t_time step.
- Creat screenshots by copying the draw window or by using the best ray tracer on the net: Povray.
Creat movie scene is also supported - Generat Mesh files that describe the shape of the mathematical model.
Supported formats are:
- Povscript : Povray is the best ray tracer available on the net...and it's free.
- VRML2: to use with the majority of current browsers via an appropriate plug-in.
- OBJ: a well-known file format supported by the majority of 3D applications (Blender, MAYA and Moray...).
K3DSurf Usage
K3DSurf can be used by every one interested in 3D Mathematical drawing functions and don't require any special competences by users. Most of the work was done with the intention to make K3DSurf as simple as possible but without any harm of it's efficiency:
- K3DSurf program is developed for being used by beginner users with low level degree in Mathematical science simply by testing examples (more than 50) given with it and by rendering them with Povray.
Add/remove some functions from equations and visualize new results is the best way to understand 3D mathematical functions behaviours.
- 2D and 3D Designers: Pov scripts (and other file formats) generated by K3DSurf can also be integrated in complicated scenes. Adding textures to mesh objects under Povray, for examples, is straightforward.
- Teachers and height level students can study very complicated surfaces with K3DSurf. 4D/5D hyperobjects is another field where talented competences can give their best to discover new entity with artefacts that are not obvious to understand for a neophyte.
K3DSurf Overview
Parametric Surface/curve :
K3DSurf use parametric descriptions of it's physical models. The parametric method of representing surfaces/curves uses a function to map some portion of R2 (the domain) to a patch of the surface in R3.
Because any position in the plane, and thus any position on the surface patch, can be uniquely given by two coordinates, the surface is said to be parameterized by those coordinates.
Parametric equations can be either “Implicit” or “Explicit”:
** Explicit equations:
In an explicit equations, x, y, and z are each given by separate functions of parameters u and v.
Example: X =u, Y = u+v, Z = cos(u+v)
** Implicit equations: Right now, only implicit equations like Z^n = f(X,Y) with (n mod 2 = 1) are supported by K3DSurf.
Example: Z = exp(x^2 + y^2), Z^7 = exp(x*cos(y))...
Because any position in the plane, and thus any position on the surface patch, can be uniquely given by two coordinates, the surface is said to be parameterized by those coordinates.
Parametric equations can be either “Implicit” or “Explicit”:
** Explicit equations:
In an explicit equations, x, y, and z are each given by separate functions of parameters u and v.
Example: X =u, Y = u+v, Z = cos(u+v)
** Implicit equations: Right now, only implicit equations like Z^n = f(X,Y) with (n mod 2 = 1) are supported by K3DSurf.
Example: Z = exp(x^2 + y^2), Z^7 = exp(x*cos(y))...
K3DSurf defined functions:
| Function | Symbol |
| Sine | sin() |
| Cosine | cos() |
| Tangent | tan() |
| Arc Sine | asin() |
| Arc Cosine | acos() |
| Arc Tangent | atan() |
| Hyperbolic Sine | sinh() |
| Hyperbolic Cosine | cosh() |
| Hyperbolic Tangent | tanh() |
| Inverse Hyperbolic Sine | asinh() |
| Inverse Hyperbolic Cosine | acosh() |
| Inverse Hyperbolic Tangent | atanh() |
| Natural Logarithm | log() |
| Logarithm base 10 | log10() |
| Angle | angle() |
| Absolute Value / Magnitude | abs() |
| Secant (equivalent to 1/cos()). | sec() |
| Cscant (equivalent to 1/sin()). | csc() |
| Cotant (equivalent to 1/tan()). | cot() |
| Modulus | mod() |
| Square Root | sqrt() |
| Exponential | exp() |
| Min(A,B) | min(A,B) |
| Max(A,B) | max(A,B) |
| Rounds to the closest integer | int() |
| Constants | pi |
User defined functions :
You can define your own function by using «Function definition" area in "More Option" page.
Exemple :
k(u,v,t,x,y) = sin(u)*cos(v)*t*x
X = u
Y = cos(v)*k(u,v,t,x,y) <-- cos(v)*[sin(u)*cos(v)*t*x]
Z = cos(u)
You can also use the function "k" for more complicated purpose like:
X = u
Y = v
Z = k(exp(u)*t,u,v,t,t) <-- sin(exp(u)*t)*cos(u)*v*t
NB: The definition of the function k use (u,v,t,x,y) parameters which are different compared to (u,v,t,x,y) used in parametric equations.
Exemple :
k(u,v,t,x,y) = sin(u)*cos(v)*t*x
X = u
Y = cos(v)*k(u,v,t,x,y) <-- cos(v)*[sin(u)*cos(v)*t*x]
Z = cos(u)
You can also use the function "k" for more complicated purpose like:
X = u
Y = v
Z = k(exp(u)*t,u,v,t,t) <-- sin(exp(u)*t)*cos(u)*v*t
NB: The definition of the function k use (u,v,t,x,y) parameters which are different compared to (u,v,t,x,y) used in parametric equations.
Animation and Morph :
** Animation consists in 3D rotation of the object.
Direction and speed of the rotation are controlled with Mouse Button direction and speed.
** Morph consists on the introduction of new parameter “t” inside parametric equations.
Example:
X = u
Y = v
Z = sin(pi*((u)^2+(v)^2))/2 ==> sin(t*pi*((u)^2+(v)^2))/2
You have to click « calculate » button to register the new equation.
Now, activate Morph effect (basic-->AimationAndMorph-->Morph). You can also combine Animation and Morph effects. In addition, you can control CPU usage and t_step in “More Option” page.
Direction and speed of the rotation are controlled with Mouse Button direction and speed.
** Morph consists on the introduction of new parameter “t” inside parametric equations.
Example:
X = u
Y = v
Z = sin(pi*((u)^2+(v)^2))/2 ==> sin(t*pi*((u)^2+(v)^2))/2
You have to click « calculate » button to register the new equation.
Now, activate Morph effect (basic-->AimationAndMorph-->Morph). You can also combine Animation and Morph effects. In addition, you can control CPU usage and t_step in “More Option” page.
0 comments