How ot use (Manual for the software GEOMECA 4e )


The upgraded GEOMECA 4e (version 4.1) HTML Help is in one HTML Help in Korean and English. (It's in the product.)

Within the program, you can use it by switching to Korean or English, like version 5.


The HTML Help for the upgraded GEOMECA 5 (version 5.0) was created first only in Korean. (It's in the product.)

You can use it by converting it into Korean or English within the program.



Click the three buttons below to see a screenshot of HTML Help.



How to use: [Ver 4.0]



The 1st: Drawing the graph of functions; 1 - line, point, cylindrical unit



   Two regular octahedrons

   - Ray trace

   - opacity, semitranceparancy


The 2nd: Drawing the graph of  functions; 2 - a function defined by intervals


The 3rd: Drawing other graphs; 3 - using figure tools


The 4th: Drawing the graph of  functions; 4 - surface


The 5th: Drawing other graphs; 5 - pentagonal prism (using commands)


The 6th: Trace of fucntion values of a curve or a surface


The 7th: Drawing a graph by transforming


The 8th: To use the collection of executed formulas and a picture collection screen; 1


The 9th: To use a picture collection screen; 2 and print, save


The 10th: Making lines to be rotated using the muli-line of figure tools and makiing a body of rotation


The 11th : To use differentiation


The 12th: To use complex numbers, integral, parametric (multivariable) function formulas, scientic calculation and other calculations


The 13th: To use matrix calculation



The 14th: To perform statistical calculations



The 15th: To draw included functions; To apply the basic editing of pictures



   Function (Picture explanation): What's new in version 4.0 ?


Expression input

Rectangular coordinates


2 dim

Negative f(x,y)=0

 3-dimensional solid curve can be made.

  3-dimensional surface: perfectly


3 dim

Negative f(x,y,z)=0

Polar coordinates


2 dim

Negative   f(r,u)=0

Sphere coordinates

Cylindrical coordinates


3 dim

Parametric r=f(u): p=g(u):  z=h(u)


3 dim

Parametric r=f(u,v): p=g(u,v):  z=h(u,v)

Other figures


2,3 dim


Surface solid

2,3 dim


Figure Tools: Drawing things such as basic figures, functions, quadric curves, etc. in 2- or 3-dimensional coordinates by using the mouse.

A body of rotation - Rotating lines that are drawn by the function-expression or figure tools or commands.

  Making a body of rotation centering around  the rotation-axis which is the axis of x, y, z or any line or the line through two points  appointed by the angle and subdivision.

The drawing screen

Adjusting the size of coordinates region

 2-dimensional coordinates

The method displaying 2- dimensional coordinates

Displaying the polar coordinates

Displaying the arrowheads: auto-option

Displaying  the origin, axis, coordinates values

 auto - option

The method displaying 3-dimensional coordinates

Drawing the space-frame, the coordinates-axis


Displaying a full line or a dotted line of  the space- frame temporarily

(Not) displaying middle lines of the surface of the space-frame

Making selected items be continuously seen when we let the space-frame be rotated (animation)

Displaying coordinates values

auto - option

Equally dividing interval of variable range; adjusting subdivision of figure for velocity, accuracy, good picture

4.0 can re-adjust  the rectangular region with the mouse

Drawing method


point unit

surface unit

cylinder unit (hidden surface removal)

rectangular, cubic unit

ray trace

a body of rotation (hidden surface removal)

a body of rotation ( surface unit)


point unit

line unit

only toward one variable direction

negative - cross section perpendicular to the x-axis

negative - cross section perpendicular to the y-axis

negative - cross section perpendicular to the z-axis

surface unit

hidden surface removal

cubic unit

ray trace

color of solid surface


by black, white

by the color of dialogue box (appointed color)

by brightness

by illumination

by the color of dialogue box (appointed color( not  to distinguish faces)

transparently (distinguishing face)

shape of solid surface


Triangle -The polygon is subdivided to triangles.

Polygon - leave as it is.

illumination - in case of drawing  3-dimensional solid,  direction of light and intensive of light is adjustable.

          also appointing the effect of shadow,  transparency of light  and the index of refraction and the ratio of reflection.

appointing the color

background of 'the drawing screen', coordinate axis, internal color of figure

section coordinate, coordinate scale - appointment, auto option

separately appointing color of character in 2D or 3D screen.

appointing line-thickness


Graph or figure, coordinate axis, space-frame

8 ~ 14

section coordinate, coordinate scale - appointment, auto option


coordinate scale - appointment, auto option


 a dotted line

picture collection screen

In case of saving pictures by gcg file , the bmp files is saved in the folder which is made below the gcg file..

  (Management  becomes convenient.)

Making the 'temporary graph memory display window' or  the contents above it  to be seen in a big window


inverse trigonometric function, hyperbolic function, inverse hyperbolic function, sgn, conj


Single Integral (indefinite integral)

differentiation(derivative), high order differentiation, partial differentiation

differential coefficient, high order differential coefficient , partial differential coefficient

in the field of complex numbers - included complex operation and function

calculation without regard to ciphers - decomposition to prime factors, nPr, nCr,  nHr, n!, +,-,*,/, sqr

Matrix - sum, difference, product, scalar  multiple, inverse matrix, determinant, cofactor matrix, transpose matrix, the echelon matrix, the solution  of linear equation, alternating product

statistic analysis