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threedkit(7) Svgalib User Manual threedkit(7)
NAME
threedkit - a set of functions for 3D support.
DESCRIPTION
The 3dkit consists mainly of the following triangle functions
gl_striangle(3), gl_swtriangle(3), gl_triangle(3),
gl_trigetcolorlookup(3), gl_trisetcolorlookup(3),
gl_trisetdrawpoint(3), gl_wtriangle(3).
Beware, these functions are not a direct part of the svgalib library.
Instead their source is part of svgalib and can be found in the
threeDkit/ subdirectory of the original svgalib distribution. However,
it is not installed in the system by default, s.t. it is unclear where
you can find it if your svgalib was installed by some linux
distribution.
In case of any such problem, simply get an svgalib distribution from
the net. You even don't need to install it. Just make in the threeDkit/
subdirectory. As of this writing, svgalib-1.2.12.tar.gz is the latest
version and can be retrieved by ftp from sunsite.unc.edu at
/pub/Linux/libs/graphics and tsx-11.mit.edu at /pub/linux/sources/libs
which will most probably be mirrored by a site close to you.
The functions are defined in the tri.o and triangl.o files (or their
resp. sources) which you must link to your program.
EXPLANATION ON 3DKIT.C
This is main engine for 3D rendering.
Program flow:
1. The function called from outside of 3dkit.c is TD_drawsolid.
This first calculates the rotation matrix from the camera
rotation angles (see below for more details). It then allocates
memory for the temporary array for holding temporary coords in
subsequently called functions. It also sorts the surfaces from
furthest to closest; according to the distance of the centre
grid-point of each surface from the camera.
It also establishes whether ROTATE_OBJECT option is on and
zero's the camera position if so --- this is for displaying the
object at the screen centre like in a 3D CAD package, as apposed
to virtual reality where the object can be anywhere and the
actual camera position can move.
In the case of ROTATE_OBJECT being on, although the camera
position is zero, some distance has to be placed between the
camera and the object (or else it would appear to be infinitely
large on the screen). This is done using the variable s_cam
which is initialized to distance which is set by the calling
application. It then loops through each surface (ordering them
in the way they were just sorted --- i.e. according to sortarray
indexing) and calls one of five graphic routines to write the 3D
surface to the hardware.
2. Assume that TD_drawsolid then calls TD_drawmesh. Here, each
surface grid point is first TD_translate'd into a 2D screen
point and stored in the temp array. There are obviously
w(idth)*h(eight) points in the grid.
Following, each line from the 2D temp array is drawn on the
screen. To draw the surface, the corner wishbone (two lines)
from each grid square is drawn while advancing across and the
down. After completing the scan, the furthest two edges of the
surface must then be filled in, vis.:
_ _ _ _ _ _
|_|_|_|_|_|_
|_|_|_|_|_|_
|_|_|_|_|_|_
|_|_|_|_|_|_
|_|_|_|_|_|_
| | | | | |
To understand the object rotation, a knowledge of matrix
multiplication is required. I once derived a camera rotation
before I learned matrix computation. It amounted to the same
thing, but was unnecessarily complicated to optimise.
3. TD_translate called from TD_drawmesh (and others) converts from
the 3D grid point coordinate to the 2D screen coordinate using:
(a) the three camera position coordinates, (or the single camera
distance value, s_cam, if ROTATE_OBJECT is set), and (b) the
three camera rotation angles. However, the three camera rotation
angles have already been converted into a rotation matrix when
TD_calc_rotation_matrix was called by TD_draw_solid.
To convert from a 3D coordinate to a 2D screen coordinate, the
camera position (or more correctly, the position of the object
from the camera) must first be added to each of the 3D grid
coordinates. If the user has chosen to use 32 bit values for
the discription of the surface, then these must be right shifted
to the same size as the 16 bit case.
x, y and z now hold the 3D position of the object relative to
the camera centre (or in these terms, the centre of the video
screen RIGHT ON the screen). The vector [x y z] must now be
multiplied by the rotation matrix. The xt value must also have
the camera distance, s_cam, added to it in case the
ROTATE_CAMERA is set (in which case x_cam, y_cam and z_cam (the
camera position) will be zero and instead s_cam will have a
value to provide the necessary object-camera distance). A test
is also made as to whether this value is zero or negative. In
the case, the point is too close to the camera, or behind the
camera, and must not be drawn.
After the multiplication, the resulting vector [xt yt zt] has
been rotated to be aligned with screen. The vector is now
adjusted for perspective by dividing the yt and zt values
(horizontal and vertical respectively) by the xt value (into the
screen). Division is done by muldiv64 because the intermediate
product is larger than 32 bits. xscale and yscale are factors
that scale the image to size. posx and posy is just the centre
of the screen, or more precisely:
The exact position of the pinhole camera viewing the object.
4. TD_calc_rotation_matrix calculates the nine entries of the 3 by
3 matrix used in TD_translate. In order that only integer
arithmetic is performed, these values are stored and used as
integers. Since this matrix's entries are always between -1 and
+1, they have to be integer left shifted to give them accuracy.
TD_MULCONSTANT scales them to sufficient bits of accuracy before
they are converted to integers.
This also means that results (of multiplications with them) have
to be scaled down by the same amount. This scaling is inherent
in the final multiplication and division (muldiv64) done in the
TD_translate function, so an extra division is not consumed.
The rotation matrix effectively rotates the vector by the
Eulerian angles alpha, beta and gamma. These angles represent
successive rotations about each of the 3D axes. You can test
which angles do what by looking at the calling application.
Their precise definitions are not all that important since you
can get the keyboard to do the right thing with a little trial
and error.
Intrisics of drawing non-transparent surfaces...
to be continued ?!
SEE ALSO
vgagl(7), svgalib(7), gl_striangle(3), gl_swtriangle(3),
gl_triangle(3), gl_trigetcolorlookup(3), gl_trisetcolorlookup(3),
gl_trisetdrawpoint(3), gl_wtriangle(3), plane(6), wrapdemo(6).
AUTHOR
This manual page was edited by Michael Weller <eowmob@exp-math.uni-
essen.de>. The demos, the initial documentation and the whole threedkit
stuff was done by Paul Sheer <psheer@icon.co.za>.
Paper mail:
Paul Sheer
P O BOX 890507
Lyndhurst
Johannesburg 2106
South Africa
Donations (by check or postal order) will be appreciated and will
encourage further development of this software. However this is
strictly on a voluntary basis where this software falls under the GNU
LIBRARY GENERAL PUBLIC LICENSE.
Svgalib (>= 1.2.11) 2 Aug 1997 threedkit(7)