Conference rusure::math

    Hi.
    Well, I deleted those drawings a long time ago, then replaced them
    with 3-D pendulum drawings, then deleted those, and now someone
    wants an example.
    
    The following 3 replies are 3-dimensional parallax perspective
    line drawings of an imaginary pendulum with independent X,Y,and
    Z oscillations (sort of a 3-D lissajous).  The point triples
    were generated with sine function in BASIC; the ReGIS drawings
    were done in parallax and perspective with an Ada program.
    I wrote the software.
    
    The next three replies are sixel.  You can SAVE TT to see them
    on a VT125,VT240,VT241, or compatible.
    
    Tom

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    I'm sorry. I got mixed up.  
    The next reply is from the Pascal surface grapher.
    Tom

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PROGRAM surface(vector_file);
{ Tom janzen probably January 1986, but now is 7-13-88 }
{ Digital Equipment Corporation }
{ Edit the source below to use the surface equation you want, and compile
  and link it.  Run it to generate graph_data.dat for the other program
  three_d_graph.pas.}
{_______________________________________________________________________}
CONST
    max_side = 20;
VAR
    X_Index, Y_Index : INTEGER;
    x,y,f : REAL;
    vector_file : TEXT;

PROCEDURE Write_Schedule_to_File;
    BEGIN
    OPEN(vector_file, 'graph_data.Dat', 
	History := NEW);
    REWRITE(vector_file);
	    WRITELN(vector_file,' ',max_side);
	    WRITELN(vector_file,' ',max_side);
    for x_index := 1 to max_side do
        for y_index := 1 to max_side do
        begin
            x := (x_index-(max_side/2))/(max_side/2);
            y := (y_index-(max_side/2))/(max_side/2);

{***********************************************************************}
{******Remove comments to use one of the following surface equations****}
{           f := sin(2*(x+y));					}
            f := sin(2*(x**2 + y**2));
{           f := sin(6*(x**2 + y**2))/(x**2 + y**2 + 0.01);	}
{	    f := sin(12*y+x);					}
{           f := cos(15*(y**2 + x**2))/exp(y**2 + x**2);	}
{           f := cos(10*((Y+0.7)**2+(x+0.7)**2))/exp((Y+0.7)**2+(x+0.7)**2);}
{	    f := COS(10*y)+SIN(10*X);				}
{***** END OF SURFACE EQUATION BLOCK}


	    WRITELN(vector_file,' ',f)
        end;
    CLOSE(vector_file)
    END;

{----------------------------------------------------------------------}
{                      M A I N   P R O G R A M                         }
{______________________________________________________________________}
BEGIN
            Write_Schedule_to_File;
END.

PROGRAM Three_D_Graph (INPUT, OUTPUT, Graph_Data, Graph_Plot);
{
PROGRAM DESCRIPTION: 
 
	This program will write ReGIS commands to 
	a file called Graph_Plot to make 
	graphs on a ReGIS terminal of
	data stored in a TEXT file called Graph_Data.
	The input file is a TEXT file of REAL numbers.  
	The first number in Graph_Data is the number of X coordinates.
	The next number is the number of Y coordinates.
	The following array is a Z(X, Y) value array in this order:
	Z(1,1) Z(1,2) Z(1,3)... 
AUTHOR: 
 
	Thomas E. Janzen
 
CREATION DATE:	23-JAN-86
}
 
CONST
    Points_Per_Line = 11;
    Maximum_Matrix_Width = 30;
    {Video Control Characters follow.}
    Escape = CHR(27);
    VT100_Erase = '[2J'; {Must be preceded by Escape.}
    Enter_Regis	 = 'P1p'; {Must be preceded by Escape.}
    Regis_Erase = 'S(E)';
    {To move the ReGIS graphics cursor to a point, 
	WRITE(Point,integer:3,comma,integer:3,Right_Bracket);}
    Point = 'p[';
    {To draw a line from the current cursor position,
	WRITE(Vector,Left_Bracket,integer:3,comma,integer:3,Right_Bracket);}
    Vector = 'v';
    Comma = ',';
    Right_Bracket = ']';
    Left_Bracket = '[';
    Exit_Regis = '\'; {Must be preceded by Escape.}
    X_Resolution = 767; {The screen has this many pixels across.}
    Y_Resolution = 478; {The screen has this many pixels vertically.}
    { Flip over the Y because Screen Y coordinates are upsidedown.}
    Front_of_Table = Y_Resolution; {The location on screen of the
	front of an imaginary table that the graph appears to rest on.}
    Back_of_Table = Y_Resolution/2; {The back of the imaginary table
	the graph rests on.}
    Pi = 3.14159265358979;
    Angle_of_Incline = Pi/3; {The angle of the sides of the table with the
	horizontal.}
    Upper_Stage_Right_Indent = 
	COS(Angle_of_Incline)  *  (Y_Resolution / SIN(Angle_of_Incline) );

VAR
    { The TEXT file Graph_Data must exist when the program starts.
	It holds REAL numbers which represent the
	numeric data to be represented.  The first number is the number of
	equal interval X values for the matrix.  The second number is the
	number of equal interval Y values.  The following values are the
	Z data, with Y coordinate varying most quickly.
	The TEXT file Graph_Plot is produced by the program.  It holds
	ReGIS (Remote Graphics Instruction Set) commands to draw the graph
	on a ReGIS (VT240 or VT125) terminal.}
    Graph_Data, Graph_Plot : TEXT;
    {Number_of_X and Number_of_Y are the first two numbers read from
	Graph_Data, and represent the number of discrete, equal interval
	values for X and Y, which are the independent variables for
	f(Z) = f(X,Y)}	
    Number_of_X,
    Number_of_Y,
    {Acrosses is an index counter for drawing the z=f(x) curves at each
	fixed Y.}
    Acrosses,
    {Ups is an index counter for drawing the z=f(y) curves at each fixed X.}
    Ups,
    {Outside_Index and Inside_Index are ordinary loop index counter 
	identifiers.}
    Outside_Index,
    Inside_Index,
    {Points is a loop index counter to count the points along a single curve.}	
    Points,
    {X_ and Y_ Index are loop index counters used to point to matrix values.}
    X_Index,	Y_Index,
    {Min_Z_X_Index is the first index of two that points to the minimum
	value in Z.  Min_Z_Y_Index is the second.}
    {Max_Z_X_Index is the first index of two that points to the Maximum
	value in Z.  Max_Z_Y_Index is the second.}
    Min_Z_X_Index,	Min_Z_Y_Index,	Max_Z_X_Index,	Max_Z_Y_Index
    : INTEGER := 1;
    Number_of_Points_Written 
    : INTEGER := 0;
    {Z_Range is the range of Z (Zmax - Zmin).  Z_to_Pixel_Ratio
	is the range of Z between screen pixels.}
    Z_Range, Z_to_Pixel_Ratio 
    : REAL := 0;
    {Z is the array that holds the data to be plotted.  It is read 
 	from Graph_Data.}
    Z : ARRAY [ 1..Maximum_Matrix_Width, 1..Maximum_Matrix_Width] OF
	    REAL;
    {Z_Screen_X is an array of horizontal screen coordinates for each
	member of Z, corresponding.}
    {Z_Screen_Y is an array of vertical screen coordinates for each
	member of Z, corresponding.}
    Z_Screen_X, Z_Screen_Y : ARRAY 
	[1..Maximum_Matrix_Width, 1..Maximum_Matrix_Width] OF INTEGER;
{-----------------------------------------------------------------------}
{		M A I N   P R O G R A M					}
{-----------------------------------------------------------------------}
BEGIN {Main Program}
{Read the File into the values and the array}
OPEN(Graph_Data, 'Graph_Data.dat', History := OLD); {This file exists at start.}
RESET(Graph_Data);
READ(Graph_Data, Number_of_X, Number_of_Y); {Find out how many data to read.}
FOR Outside_Index := 1 TO Number_of_X DO
    FOR Inside_Index := 1 TO Number_of_Y DO
        READ(Graph_Data, Z[Outside_Index, Inside_Index]); {Read Z.}
{Find the minimum and maximum Z.}
FOR Outside_Index := 1 TO Number_of_X DO
    FOR Inside_Index := 1 TO Number_of_Y DO
	BEGIN
	IF Z[Outside_Index, Inside_Index]<Z[Min_Z_X_Index, Min_Z_Y_Index ] 
        THEN
            BEGIN {If there is a lower number in Z, update the 
	    minimum's indices.}
            Min_Z_X_Index := Outside_Index;
            Min_Z_Y_Index := Inside_Index
            END;
        IF Z[Outside_Index, Inside_Index]>Z[Max_Z_X_Index, Max_Z_Y_Index ]
        THEN
            BEGIN {If there is a higher number in Z, update the 
			maximum's indices.}
                Max_Z_X_Index := Outside_Index;
                Max_Z_Y_Index := Inside_Index
            END;
	END;
    {Find the Scale, the Proportion}
    Z_Range := Z[Max_Z_X_Index, Max_Z_Y_Index]-Z[Min_Z_X_Index, Min_Z_Y_Index];
    Z_to_Pixel_Ratio := (Z_Range/Back_of_Table)*1.5;
    {Create array of the screen coordinate points.}
    FOR X_Index := 1 TO Number_of_X DO
	FOR Y_Index := 1 to Number_of_Y DO
	BEGIN {include angular shift to the right}
	    Z_Screen_Y[X_Index, Y_Index] := 
		ROUND(((Front_of_Table) - (((Z[X_Index, Y_Index]-
	        Z[Min_Z_X_Index, Min_Z_Y_Index])/Z_to_Pixel_Ratio)
			+(Front_of_Table-Back_of_Table)*
			(Y_Index-1)/(Number_of_Y-1))));
	    Z_Screen_X[X_Index, Y_Index] := 
		ROUND((((x_resolution-upper_stage_right_indent)
		/(number_of_x-1)*(X_Index-1))+
		(Upper_Stage_Right_Indent/(Number_of_Y-1)*(Y_Index-1))))
	END;
{Initialize Terminal}
{Clear Screen}
OPEN(Graph_Plot, 'Graph_Plot.dat', History := NEW);
REWRITE(Graph_Plot);
WRITELN(Graph_Plot, Escape, VT100_Erase);
{Put terminal in Regis mode.}
WRITELN(Graph_Plot, Escape, Enter_Regis);
WRITELN(Graph_Plot, Regis_Erase);
{Draw the square on the bottom of the stage.}
WRITE(Graph_Plot, Point, '000', Comma, Front_of_Table:3, Right_Bracket);
WRITE(Graph_Plot, Vector, Left_Bracket, 
	X_Resolution-Upper_Stage_Right_Indent:3, Comma,
	Front_of_Table:3,Right_Bracket);
WRITE(Graph_Plot, Left_Bracket, X_Resolution:3, Comma, Back_of_Table:3, 
	Right_Bracket);
WRITELN(Graph_Plot, Left_Bracket, Upper_Stage_Right_Indent:3, Comma, 
	Back_of_Table:3,
	Right_Bracket);
WRITELN(Graph_Plot, Left_Bracket, '000', 
	Comma, Front_of_Table:3, Right_Bracket);
{Draw with either sharp or smooth lines}
FOR Acrosses := 1 TO Number_of_Y DO
{The curves that go left to right.}
    BEGIN
    WRITELN(Graph_Plot);
    {Position the cursor at the left end of the graph.}
    WRITE(Graph_Plot, Point, Z_Screen_X[1, Acrosses]:3, Comma, 
	Z_Screen_Y[1, Acrosses]:3, Right_Bracket,Vector);
    FOR Points := 2 TO Number_of_X DO
        BEGIN
        Number_of_Points_Written := Number_of_Points_Written + 1;
        IF Number_of_Points_Written MOD Points_Per_Line = 0 
        THEN WRITELN(Graph_Plot) ELSE {do nothing};
        WRITE(Graph_Plot, 
	Left_Bracket, Z_Screen_X[Points, Acrosses]:3, Comma, 
            Z_Screen_Y[Points, Acrosses]:3, Right_Bracket)
        END;
    END;
{Draw the curves that go bottom to top.}
FOR Ups := 1 TO Number_of_X DO
BEGIN
    {Position the cursor at the bottom end of the graph at the right point.}
    WRITELN(Graph_Plot);
    WRITE(Graph_Plot, Point, Z_Screen_X[Ups, 1]:3, Comma, 
        Z_Screen_Y[Ups,1]:3, Right_Bracket,Vector);	
    FOR Points := 1 TO Number_of_Y DO
    BEGIN
        Number_of_Points_Written := Number_of_Points_Written + 1;
        If Number_of_Points_Written MOD Points_Per_Line = 0 THEN WRITELN(Graph_Plot) ELSE {do nothing};
        WRITE(Graph_Plot, Left_Bracket, Z_Screen_X[Ups, Points]:3, Comma, Z_Screen_Y
		[Ups, Points]:3,
		Right_Bracket)
    END
END;
WRITE(Graph_Plot, Escape, Exit_Regis)
END.