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Chapter 4
Coordinate Systems
58 Fastgraph User's Guide
Overview
Fastgraph uses three coordinate systems to perform text and graphics
output -- character space, screen space, and world space. Character space is
used in text modes and optionally for displaying character strings in graphics
modes. Screen space is the basic coordinate system for graphics video modes
and uses the screen's physical device coordinates. Viewports are an extension
of screen space that let you assign an alternate integer-based coordinate
system to rectangular subsets of the screen. Finally, world space is a user-
definable coordinate system for graphics modes that uses floating point
values. The world space coordinate system is not available in Fastgraph/Light.
Character Space
The coordinate system used for displaying characters is called character
space. Fastgraph uses character space for displaying characters in both text
and graphics video modes (you can also use screen space to display characters
in graphics modes). Character space can be thought of as a grid of rows and
columns, with each cell in the grid holding one character. Each cell is
identified by its unique (row,column) integer coordinates. The rows and
columns are numbered starting at zero; the origin is always the upper left
corner of the screen. For example, in the 80-column by 25-row text modes (2,
3, and 7), the default (row,column) coordinates of the screen corners are
shown in the following diagram.
(0,0) (0,79)
(24,0) (24,79)
The number of rows and columns depends on the video mode, as shown in the
following table. For graphics modes, the table also includes the width and
height in pixels of a character cell.
Mode No. of No. of Char. Char.
Number Columns Rows WidthHeight
0 40 25
1 40 25
2 80 25
3 80 25
4 40 25 8 8
5 40 25 8 8
6 80 25 8 8
7 80 25
9 40 25 8 8
11 80 25 9 14
12 40 25 8 8
13 40 25 8 8
14 80 25 8 8
15 80 25 8 14
Chapter 4: Coordinate Systems 59
16 80 25 8 14
17 80 30 8 16
18 80 30 8 16
19 40 25 8 8
20 40 25 8 8
21 40 50 8 8
22 40 30 8 8
23 40 60 8 8
24 80 25 8 16
25 80 30 8 16
26 100 37 8 16
27 128 48 8 16
28 100 37 8 16
29 128 48 8 16
Fastgraph includes two routines, fg_getmaxx and fg_getmaxy, that
respectively return the maximum column and row numbers in text modes. Example
4-1 demonstrates these two routines in a text mode. The program uses
fg_getmaxx and fg_getmaxy to obtain the maximum column and row numbers in mode
3. It then displays these values (79 and 24).
Example 4-1.
#include <fastgraf.h>
#include <stdio.h>
void main(void);
void main()
{
int max_col;
int max_row;
int mode;
fg_initpm();
mode = fg_getmode();
fg_setmode(3);
max_col = fg_getmaxx();
max_row = fg_getmaxy();
fg_setmode(mode);
fg_reset();
printf("Last col = %d\n",max_col);
printf("Last row = %d\n",max_row);
}
Screen Space
Screen space is one of two available coordinate systems in graphics
modes. It uses the physical device coordinates. Screen space can be thought of
as a grid of rows and columns, with each unit in the grid holding one pixel.
Each pixel is identified by its unique (x,y) integer coordinates. The pixel
rows and columns are numbered starting at zero; the origin is always the upper
60 Fastgraph User's Guide
left corner of the screen. For example, in the 320x200 graphics modes, the
(x,y) coordinates of the screen corners are shown in the following diagram.
(0,0) (319,0)
(0,199) (319,199)
The Fastgraph routines fg_getmaxx and fg_getmaxy return the maximum x and
y screen coordinates when used in graphics modes, as shown in example 4-2. The
program uses fg_getmaxx and fg_getmaxy to obtain the maximum x and y
coordinates in the standard VGA/MCGA 256-color graphics mode (mode 19). It
then displays these values (319 and 199).
Example 4-2.
#include <fastgraf.h>
#include <stdio.h>
void main(void);
void main()
{
int maxx;
int maxy;
int mode;
fg_initpm();
mode = fg_getmode();
fg_setmode(19);
maxx = fg_getmaxx();
maxy = fg_getmaxy();
fg_setmode(mode);
fg_reset();
printf("(%d,%d)\n",maxx,maxy);
}
Viewports
Viewports provide an alternate integer-based coordinate system for
referencing pixels. Fastgraph includes routines to create a viewport, return
the viewport limits, and convert viewport coordinates to their screen space
values.
A viewport definition consists of its extremes in "viewport space" and
the corresponding limits in screen space. The fg_setview routine defines a
viewport. Its first four parameters represent the minimum x, maximum x,
minimum y, and maximum y viewport coordinates, and its last four parameters
represent the corresponding screen space pixel values defining the viewport's
physical size and location. For example, the call
Chapter 4: Coordinate Systems 61
fg_setview(100,739,100,499,0,159,0,99);
would create a 640x400 viewport in the upper left corner of a 320x200 screen.
The viewport's coordinates would range from 100 to 739 horizontally and 100 to
499 vertically. In other words, the viewport coordinate (100,100) would map to
the screen space pixel (0,0). The following diagram illustrates this viewport.
The viewport space coordinates appear in boldface, while the other values are
the equivalent screen space coordinates.
(100,100) (739,100)
(0,0) (159,0) (319,0)
(0,99) (159,99)
(100,499) (739,499)
(0,199) (319,199)
Fastgraph's fg_getview routine returns the current viewport limits and
corresponding screen space limits, as defined in the most recent call to
fg_setview.
Once you've defined a viewport, the fg_xview and fg_yview functions
translate viewport coordinates to their screen space equivalents. The
translated values can then be passed to any Fastgraph routine that expects
screen space coordinates. For example, Fastgraph's fg_rect routine draws a
filled rectangle in screen space. If you wanted to fill the viewport defined
above with color 10 pixels, you could do this as follows:
fg_setcolor(10);
fg_rect(fg_xview(100),fg_xview(739),fg_yview(100),fg_yview(499));
Example 4-3 demonstrates a simple use of viewports in the standard
320x200 VGA/MCGA 256-color graphics mode. After filling the screen with white
(color 15) pixels, it sets up a viewport in the upper left quadrant of the
screen and uses fg_rect to fill it with light blue (color 9) pixels. It then
defines three new viewports in the other screen quadrants, similarly filling
the upper right quadrant with light green (color 10) pixels, the lower left
quadrant with light cyan (color 11) pixels, and finally the lower right
quadrant with light red (color 12) pixels. Note how the same viewport
coordinates are used to fill the viewport in each case; only the viewport
position changes.
Example 4-3.
#include <fastgraf.h>
void main(void);
void main()
{
int mode;
62 Fastgraph User's Guide
fg_initpm();
mode = fg_getmode();
fg_setmode(19);
fg_setcolor(15);
fg_rect(0,319,0,199);
fg_waitkey();
fg_setview(0,639,0,399,0,159,0,99);
fg_setcolor(9);
fg_rect(fg_xview(0),fg_xview(639),fg_yview(0),fg_yview(399));
fg_waitkey();
fg_setview(0,639,0,399,160,319,0,99);
fg_setcolor(10);
fg_rect(fg_xview(0),fg_xview(639),fg_yview(0),fg_yview(399));
fg_waitkey();
fg_setview(0,639,0,399,0,159,100,199);
fg_setcolor(11);
fg_rect(fg_xview(0),fg_xview(639),fg_yview(0),fg_yview(399));
fg_waitkey();
fg_setview(0,639,0,399,160,319,100,199);
fg_setcolor(12);
fg_rect(fg_xview(0),fg_xview(639),fg_yview(0),fg_yview(399));
fg_waitkey();
fg_setmode(mode);
fg_reset();
}
To make a viewport a "true" viewport, it is often desirable to establish
clipping limits at the viewport's extremes. This way, Fastgraph's functions
that support clipping will only draw within the viewport itself. The following
call to fg_setclip will establish the desired clipping limits:
fg_setclip(fg_xview(100),fg_xview(739),fg_yview(100),fg_yview(499));
The fg_setclip routine will be described in more detail in Chapter 6.
World Space
World space is the other available coordinate system in graphics modes.
It utilizes user-defined floating point coordinates. Fastgraph translates
world space coordinates into physical device coordinates (screen space), and
because of this it is somewhat slower than using screen space. World space can
be thought of as a standard cartesian plane extending from the lower left
corner of the screen. The world space vertical orientation is thus inverted
relative to screen space and viewports.
Any program that uses world space coordinates must first initialize
Fastgraph's internal world space parameters. The Fastgraph routine fg_initw is
Chapter 4: Coordinate Systems 63
provided for this purpose. The fg_initw routine has no arguments and must be
called before any other routine that uses world space coordinates.
The next step in using world space is to use the Fastgraph routine
fg_setworld to define the world space coordinates of the screen edges. The
fg_setworld routine has four floating-point arguments -- the minimum x
coordinate (left edge), the maximum x coordinate (right edge), the minimum y
coordinate (bottom edge), and the maximum y coordinate (top edge). For
example, if you define the world space coordinates with the statement
fg_setworld(-10.0,10.0,0.0,2.5);
the (x,y) coordinates of the screen corners would be defined as shown in the
following diagram.
(-10.0,2.5) (10.0,2.5)
(-10.0,0.0) (10.0,0.0)
Fastgraph includes a routine fg_getworld that returns the world space extremes
as defined in the most recent call to fg_setworld.
Example 4-4 uses fg_setworld and fg_getworld to illustrate an interesting
application of world space. This program calls another routine named redraw
(not shown) that erases the screen and draws a certain image using world space
coordinates. The program draws the image, waits for a keystroke, reduces the
world space by a factor of two in each direction, and then draws the image
again. This produces a zoom effect in which the image appears twice as large
as it was originally.
Example 4-4.
#include <fastgraf.h>
#include <stdio.h>
#include <stdlib.h>
void main(void);
void redraw(void);
void main()
{
int new_mode, old_mode;
double xmin, xmax, ymin, ymax;
fg_initpm();
old_mode = fg_getmode();
new_mode = fg_automode();
if (new_mode == 0) {
printf("This program requires graphics.\n");
exit(1);
}
64 Fastgraph User's Guide
fg_setmode(new_mode);
fg_initw();
fg_setworld(0.0,40.0,0.0,30.0);
redraw();
fg_waitkey();
fg_getworld(&xmin,&xmax,&ymin,&ymax);
fg_setworld(0.0,xmax*0.5,0.0,ymax*0.5);
redraw();
fg_waitkey();
fg_setmode(old_mode);
fg_reset();
}
Conversion Routines
Sometimes it's necessary to convert coordinates between character space,
screen space, and world space. Fastgraph includes eight conversion routines,
four for x coordinates and four for y coordinates, to perform such
conversions. These routines return the translated coordinate as their function
value.
The fg_xalpha and fg_yalpha routines convert screen space coordinates to
character space. The fg_xalpha routine converts a screen space x coordinate to
the character space column that contains the coordinate. Similarly, the
fg_yalpha routine converts a screen space y coordinate to the character space
row that contains the coordinate.
The fg_xconvert and fg_yconvert routines convert character space
coordinates to screen space. The fg_xconvert routine converts a character
space column to the screen space coordinate of its leftmost pixel. Similarly,
the fg_yconvert routine converts a character space row to the screen space
coordinate of its top (lowest-numbered) pixel.
The fg_xscreen and fg_yscreen routines convert world space coordinates to
screen space. The fg_xscreen routine translates x coordinates, while the
fg_yscreen routine translates y coordinates. Conversely, the fg_xworld and
fg_yworld routines convert screen space coordinates to world space. The
fg_xworld routine translates x coordinates, while the fg_yworld routine
translates y coordinates.
Summary of Coordinate Routines
This section summarizes the functional descriptions of the Fastgraph
routines presented in this chapter. More detailed information about these
routines, including their arguments and return values, may be found in the
Fastgraph Reference Manual.
FG_GETMAXX returns the maximum x coordinate in screen space when used in
a graphics mode. It returns the maximum column number in character space when
used in a text mode.
Chapter 4: Coordinate Systems 65
FG_GETMAXY returns the maximum y coordinate in screen space when used in
a graphics mode. It returns the maximum row number in character space when
used in a text mode.
FG_GETVIEW returns the current viewport limits and their screen space
equivalents, as defined in the most recent call to fg_setview.
FG_GETWORLD returns the current world space limits, as defined in the
most recent call to fg_setworld.
FG_INITW initializes Fastgraph's internal parameters for world space.
This routine must be called once, before any other routine that uses world
coordinates.
FG_SETVIEW defines a viewport with the specified extremes at the
specified screen space position.
FG_SETWORLD defines the world space coordinates that correspond to the
physical edges of the screen.
FG_XALPHA and FG_YALPHA convert screen space coordinates to character
space.
FG_XCONVERT and FG_YCONVERT convert character space coordinates to screen
space.
FG_XSCREEN and FG_YSCREEN convert world space coordinates to screen
space.
FG_XVIEW and FG_YVIEW convert viewport coordinates to screen space.
FG_XWORLD and FG_YWORLD convert screen space coordinates to world space.
66 Fastgraph User's Guide
