How to use (Manual for GEOMECA 5 )

How to use (Manual for GEOMECA 4e )

 

HTML Help is in one HTML Help in Korean and English. (It's in the product as well.)

  

     

Two regular octahedrons  - Ray trace  - opacity, semitranceparancy

 

(No. 1~15) of the following list box wais organized with the executed screenshots.

     

 

     

 

 

Comparison of features between versions 5 and 4e (the blue text: how to use (ver 4.0))

Table 1

functions

5

4e

Formula input

Rectangular

coordinate system

Cur ve

2D

Positive function y=f(x),  x=f(y)

 O

O

Parametric function x=f(u): y=g(u)

Implicit function f(x,y)=0

3D

Parametric function x=f(u): y=g(u):  z=h(u)

Cur ved

sur face

3D

Positive function z=f(x,y), x=f(y,z), y=f(z,x)

Parametric function x=f(u,v): y=g(u,v):  z=h(u,v)

Implicit function f(x,y,z)=0

Polar

coordinate system

Cur ve

2D

Positive function r=f(u), u=angle

Implicit function f(r,u)=0

Spherical

coordinate system

Cur ve

3D

Parametric function r=f(u): c=g(u):  p=h(u)

Cur ved

sur face

3D

Positive function r=f(u,v)

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

Cylindrical

coordinate system

Cur ve

3D

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

Cur ved

sur face

3D

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

Other shapes

Cur ve

2,3D

 Using commands - in a dialog box or input window

sur face, soliId

2,3D

 Using commands - in a dialog box or input window

 

Range, Scl, Wchr commands

X

Figure tool -

Drawing of basic shapes, functions, quadratic curves, etc. using only the mouse in 2D and 3D coordinate systems

O

(1, 7) Draw arbitrary lines (curves) - Add and delete lines (curves)

14. Using 'graph, figure information window', 15. Coordinates, section paper; grid, 16. Coordinates, coordinate axes only1, 7)

17.Polar coordinates

Half (circle, ellipse), half ellipse, oval (fan, arc)

X

Rotating body - rotation of lines drawn with functions and drawing tools, lines drawn with  commands, etc.

     Creates a rotating body at a specified angle and subdivision around the x, y, z axis and   a randomly defined straight line or a straight line passing through two specified points.

O

Transformation - Designate a graph or figure to be drawn by designating it

     (parallel movement, rotational movement, symmetrical movement,

      transformation by matrix, orthogonal projection, composite transformation, etc.)

Tracking-Tracking the position value of the graph

Zoom in/out of graph - Zoom in or out of the graph centered on the specified point   or flashing point or center of the screen

Table 2

functions

5

4e

Drawing

Screen

Adjustable to size

 O

O

Resize the coordinate system area

 2D coordinates system

 2D coordinates system

Relating to the two-dimensional coordinate system display method

Grid coordinates display

Show Coordinates Axis Only

Do not display

polar coordinates system display

Arrowhead display: Automatic and options

Display origin, axis and coordinate values

 Direct input

 Automatic and Options

Relating to the three-dimensional coordinate system display method

Draw Space frame and coordinate axis

2D

3D

Space frame (not) visible

Temporary display of dotted and solid lines in the space frame

Whether the line is displayed in the middle of the space frame surface

Draw a line to grasp the spatial location of a point

O

X

Space frame display method - parallel and perspective projection

 O

O

When the space frame is rotated, view the selected items consecutively (animation)

Arrowhead, axis display: Automatic

Display coordinate values

Direct input

Automatic (and Options)

Variable range section equalization and shape subdivision adjustment

   - Adjust for speed, accuracy, and good picture

Coordinate Axis Actual Distance Ratio Auto Options ; to 1:1

Specify the area to draw only the area to be drawn in the coordinate range

(Square area mouse control)

Character input - make the background transparent or opaque

Modify Character, move, delete, copy, paste, etc.

2D: Coordinate range including function values - Automatic adjustment

X

Create SET_Range (current coordinate range)

Character separation

-When drawing and input (to the picture collection screen), when saving (gcm)

O

Save

As bmp file: drawing screen picture only

As gcm file: Pictures, contents and pictures are saved as bmp separately

As gcd file :drawn graph only

When saving (gcm, gcg) for a reproducible formula editor's picture (formula) Check whether or not exclusion

 O

X

Edit

Copy, cut (specify area), paste (string, picture)

O

O

Paste (from formula editor)

X

Symbols...

Formula Editor...

Modify ; move ; unchecked 'RC'

character modification

O

Select, move

picture operation

X

Shape correction: unchecked 'RC'

Drawing shapes:'RC' without check mark

Delete: (Selected)

Copy and paste (selected)

Paste (related to the above two menus)

character modification, location shift: [Delete all, restore (recently deleted), string-(copy, delete, paste)]

X

O

To the very front, To the very back

O

X

Change: character background

Make the color you specify transparent

Show overlapping bottom

Tie, untie

Regenerating pictures of the formula editor

Select All

View

a Graduated ruler

O

X

Figure information of 'figure Tools'

Information on characters and figures drawn when '...RC' is unchecked state

Information of 'graph and figure' related to coordinates

Info window of 'graph and figure': To the right

Where to input the range of coordinates and variables

Only the drawing screen

Change function arangement

Frame rotation button

Screen zoom

Function name

(drawing screen) Paste Picture - as background

Language used - Korean, English

Formula input(keyboard)

Selection, Move(keyboard)

Setting of start environment

On-screen picture enlargement, reduction, inversion, view picture description

O

Picture operation (OR, XOR, AND, NOT, making the specified color transparent)

X

Drawing

method

Curve

Point unit

 O

O

line unit

face (polygon) unit

cylinder unit (hidden surface removal)

rectangle, rectangular parallelepipe unit

ray trace

rotation-body(hidden surface removal)

rotation-body(face unit)

ray trace - A frame surrounding a point

X

Curved surface

Point unit

O

line unit

In two variable directions

Only in one variable direction

Implicit function : cross section perpendicular to the x axis

Implicit function : cross section perpendicular to the y axis

Implicit function : cross section perpendicular to the z axis

face (polygon) unit

hidden surface removal

rectangular parallelepipe unit

ray trace

Color of solid surfaces

black, white

 O

O

color in the color dialogue box (With the specified color)

brightness-color in memory

illumination-color in memory

As the color (specified color) in the color dialog box (no face division)

Transparent (with face division) - frame

Shape of solid surfaces

triangle - The subdivision of the polygon that make up the face into triangles.

Polygon - Leave the point that forms the face

 

Number of vertexes of line(Cylinder type)(3~20), Blocked cylinder type

X

Lighting-Adjust the direction and intensity of light when drawing a 3D solid

     Also specify the shadow effect and light transparency and refractive and reflectance.

 O

O

3D coordinate system direction control (space frame direction control) - Can be drawn in various directions.

Direct input of rotation angle

Option button for specific direction

X

Correct the restriced area, color, and thickness of the graph you drew

O

Color designation

Graph or shape

Screen background, coordinate axis, and shape interior

Grid coordinates, coordinate scale-specified and automatic options

Specify character colors separately in 2D and 3D screen.

the inside of the figure (tool) 2

X

Line color (automatic adjustment of brightness) - Specified color, color according to brightness, and inverse of color depending on brightness

Line designation

thickness

Graphs or shapes, axes,

Space frame

1 ~ 7

 O

O

8 ~ 14

Grid coordinates, coordinate scale designation and automatic options

Length

Coordinate scale designation and automatic option

type

Solid line

dotted line

To stop in the middle of drawing, tracking, or calculating

Picture Collection Screen

Collection screen paper size adjustment

 O

O

Resize picture box to contain

existing option

B: 100% input automatic

X

Create and input and move picture boxes to contain

O

Modification Mode - Allows you to modify the contents and the picture of the selected picture box by moving it to the drawing screen.

Group file (gcg) list view : When multiple group files are created or opened, gcg files of the selected list can be viewed

View explanation contents of selected picture box

Copy, delete, and paste picture boxes

Add page, delete page, move page

Save: Save together as a gcg file, or only the selected one as a gcm file

or Only the expression for the selected one is as a gcd file

Change picture box name (individual file name)

Modify (move to formula editor), Modify (move to drawing screen)

X

Edit

Copy, paste(picture)

paste(from formula editor)

Formula editor...

Select all(current page)

copy current page(picture)

(copy)Selected pictures margin.

To the very front, To the very back

Change: character background

Make the color you specify transparent

Show overlapping bottom

Tie, untie

Regenerating pictures of the formula editor

View

Picture box name

Picture frame border

Ruler, grid settings...

Picture Collection Screen Tools Menu

Selection, Move (Keyboard)

Setting start environment

Language used (Korean, English)

Reexecution

Using the executed expression collection window

O

information window of Graph and figure related to coordinate system(temporary graph memory display window)

 Import the gcm file into the drawing screen or preserve the contents in the graph and figure information window (temporary memory display window) of the drawing screen in the modification mode on the picture collection screen (that is, add on it)

 O

View the graph, figure information window (temporary graph display window) related to the coordinate system, or the contents of the window above it in a large window

View information window of figure and character not checked in 'RC' and its contents

X

Print

Drawing screen, Picture collection screen(All, seleted pictures or group, designated page, Specifying the size and number of drawing screen picture

 O

O

Preview, Setting margin...

Designation among Background color + content, bitmap, contents; Move Coordinate value to the very front

Number of print copies, etc.

X

Coordinate Range and Scale Interval, Arbitrary Direct Entry of Variable Range, and Default Designation

O

Function

Trigonometric function, int, abs, exp, log, ln, sqr, x^y, Pi, atn

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

Draw function graph in the built-in range by double-clicked function

Table 3

functions

5

4e

 Calculation

Scientific(approximated value)

 O

O

Quotient calculation(True value)

Parmetric multi-variable function expression calculation

Single integral

Numerical integral

Indefinite integral

Double integral

Differentiation(Derivative), (High-order differential, Partial differential)

Differential coefficient, (High-order, Partial)

Calculation in complex numbers -  Complex number operations and functions included

Unlimited number of digits : prime factorization, nPr, nCr, nHr, n!, Arithmetic operation(+,-,*,/), sqr

 Matrix calculation

- Sum, Difference, Product, Scalar product, Inverse matrix, Determinant, Cofactor matrix, Transposed matrix, Echelon, solution of a simultaneous equation, alternating product of  row vectors

Data transformation - Adjust arrangement of matrix A or B, Extract columns of matrix A or B; Change the column position of matrix A or B

X

Input(keyboard)

Decomposition- LU, QR, SVD

Diagonalization of matrix, Schur Decomposition

Cross product, inner product of two row vectors; (Inner product of A and B), Length of A

Distance between A and B

Characteristic Polinomial of square matrix A

Eigenvalue, Eigenvector

Transforming the matrix A -  To Hessenberg form, To Bidiagonal form, To Frobenius form

Root of a characteristic equation(complex numbers range): Root of an equation f(z) = 0

Matrix A test - Symmetric, Skew-symmetric, Hermitian, skew-Hermitian, Unitary, Normal

Matrix, vector Norm - Euclidian, Column Norm, Row Norm, Normalization of column vectors

window arrangement

Verification display- SVD, Schur  decomposition, Diagonalization of A

Eigenvector decimal place display

Rational mumber - Decimal display method: Diaplay as decimal, Only for infinite decimal as (improper) fraction, Only for infinite decimal as (proper) fraction, Display as (improper) fraction, Display as (proper) fraction

Programming - (Matrix calculation, graphic)

 Basic commands similar to 'software basic language'

commands related with matrix and graphicasic

 Statistical calculation

File- Open, Save, Print

 O

O

Data

Data (sample) input classification

sample values,

name labels designation

- Distiction picture explanation

X

Change sample input form

Input status, sample classification method

O

(*)Function transformation

Change the position of rows and columns

Input row number

(*)Get inverse matrix

(*)matrix Cholesky decomposition: Get P like A = P'P

X

 Check items, run checked items

Check items

 Group to calculate, Horizontal - Vertical calculation

 Calculation, Graph, Frequency table

 Class interval in class-classification

Condition for region and color of a graph, characters

O

Run ckecked items

 Run the calculation

 Create frequency table

 Draw a graph

 Run Horizontal-Vertical calculationi

 Stop execution

AB-Type

1 Variable: Measure of Center - trendency, Measure of variation

Estimation, Test

2 Variables: Sample regression line, regression parabola, correlation coefficient, Estimation, Test

3 Variables: Sample regression plane, Quadratic surface. correlation coefficient, Test

C-Type

Model of regression equation

O

Regression coefficient Estimation

OLS

WLS,GLS

X

Investigation for regression models

Investigate multicollinearity between independent variables.

Investigate observations (outlier, influential).

Investigate Autocorrelation.

Residual data for independency, normality investigation

O

Estimation, Test

Variable Choice( To find best regression eqution  etc.)

Sample regression coefficient

Analysis of variance, Error term variance, Coefficient of determination, Mallow's statistic

Sample correlation coefficient

Regression coefficient, (Co)variance

Residual Variance-covariance

Fre- quency

table

Items to include in the frequency table,

Table for 1, 2, 3 variables

Graph

1 Variable

Line diagram, Histogram, Frequency polygon, Cumulative frequency function, Box diagram, Circle graph

O

Normal probability paper

X

Function, Curve - Function of povwer of test, OC Curve, probability or density function

2 Variables - Scatter diagram, Regression line, Regression parabola, Bar graph

O

3 Variables - Regression plane, Regression quadratic surface, Bar graph

For C-Type

Scatter diagram, Regression curve, Regression surface, Scatter diagram of residual, Confidence band of mean response, Prediction interval

Normal probability paper

X

Others

Distribution table, Test table

Binomial distribution

Normal distribution

Student's t distribution

Chi-square distribution

Kolmogorov - Smirnov test

F distribution (95%, 99%)

Durbin-Watson test

Table for nonparmetric methods

(A: randomness test,

B: Equality test,

C: Wilcoxen's Singed-rank test

D: Wilcoxen' Rank-
sum test,

E: Mann-Whitney U-test

F: Kruskal-Wallis test,

G: Friedman test,

H: Spearman rank-order correlation coefficient)

Calculation of distribution function

Factor experiments

O

Comparison of 'means, variance' of two normal distributions

Chi-square test

Comparison of two regression lines, Comparison of slop of two regression lines

Autocorrelation test

Nonparametric methods - median sign test, sample randomness test, equivalence test of distribution function, Wilcoxon 1 sample test, 2 sample rank-sum test, Mann-Whitney U test, Kruskal-Wallis test, Friedman Test, Rrank correlation coefficient

X

Window

Input window, Result window

 O

Table box(result window 2), Backup window

X

Table 4

functions

5

4e

Mark the area to be colored

 Function y=f(x); x=f(y)

1 General  2  y>f(x); x>f(y)   3  y <f(x); x<f(y)

4 y>f(x) or y <f(x);  x>f(y) or  x<f(y)

 O

 X

 Hyperbola, Parabola - Region with focus, Region without focus, Both above

Polygon Fillmode(A) -Alternate, Winding

Figure Fillstyle(B) - Solid, Horizontal line, Vertical line, Upward Diagonal, Downward Diagonal, Cross, Cross Diagonal

Make the overlapped lower part be viewed

y=f(x); x=f(u)l y=g(u); x=f(y);  r=f(u) Function Graph: Putting color into

Command figure: Putting color into

A, B Fixing (input in memory)

Formula Editor

File- Open, Save, Print

Sending: to the drawing screen or to the picture collection screen

Edit - Copy, Paste, Cut, Delete, Undo, Redo, Select All

View, Style, Size Definition, Form - (Template, Matrix, Row spacing) Rules

Rules can be applied in whole or individually, math functions-automatic, etc.

Help

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