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# Gouraud Shaded Polygons

By Dave Astle | Published Jul 16 1999 11:58 AM in Graphics Programming and Theory

value color step line number byte portion colors whole
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WGT Graphics Tutorial #2

Topic: Gouraud Shaded Polygons

By Chris Egerter

October 13, 1994

Contact me at: chris.egerter@homebase.com

Introduction

------------

This series of tutorials describes a method of drawing filled polygons

using 3 rendering techniques: Solid, Gouraud shading, and texture mapping.

The code in this tutorial was written in Turbo C++ but can be ported to

other graphics libraries and operating systems.  I did not use the

WGT functions in this one, so the wgtgfx.c file contains a few routines

which are needed for the demos.  I have decided to explain the method

used for these routines since I had to discover them on my own, and

think you can learn from the code.

1.0 - Shading Along a Line

--------------------------

The idea behind shading is we want different shades of color along a surface.

The simplest application of shading is along a horizontal line.  Imagine

the line is black at the left end, and white at the right end.  A pixel in

the middle will be a shade of grey.   As the line is drawn from left to

right, the color value starts at black and increases by a constant amount

towards white.  This constant value is determined by the number of colors

between the endpoints and the length of the line.  Specifically, the

constant is equal to the number of colors divided by the number of pixels

along the line.  If the number of colors equals the number of pixels,

the constant is 1, which makes perfect sense.  Since we cannot deal with

fractions of a color in computer graphics, we will only deal with the integer

portion of the color value.

2.0 - Pseudo-code

-----------------

Our basic shaded line routine looks like this:

Calculate the step value

Make a color variable equal to the left endpoint color.

For x = x1 to x2

Put pixel on screen

Add step value to the color

End for

3.0 - Assembly Language Benefits

--------------------------------

When dealing with 256 colors, you can fit the color value in one byte.

We will use fixed point math to store the step value, that is, 1 byte to

store the whole number, and 1 byte to store the fractional portion.

By using 1 byte for the fraction, we can store the whole and fractional

parts in one integer.  This makes it easy in assembly language since we

can put these values in a register, say AX, and access each portion

individually with AH and AL.  In C language you would need to shift the

value right 8 times in order to get the whole value.  This works out

perfectly since we can add a step value to AX, and AH will always contain

the color we want to put on the screen.  You don't have to worry about

the fractional portion carrying over 256 since it will already be added

to the whole portion.

4.0 - Calculating the step value in 8.8 fixed point

---------------------------------------------------

8.8 means we are using 8 bits for the number before the decimal, and

8 bits for the fraction.   You have to think of the fraction in hexadecimal

since it will carry at 256 instead of the usual decimal system most people

relate to (base 10).

To make a step value with the whole portion in the upper byte, first we

need to shift the colors to the left by 8 bits.  This will put the

color value in the high byte and leave the fraction as 0.  Now to calculate

the step value, divide it by the length.

eg:  step = (numcolors << 8) / length;

5.0 - Code segment 1

--------------------

We can write a more specific routine now:

void shadedline (int x1, int firstcolor, int x2, int lastcolor, int y)

{

int length;

int numcolors;

int colorvalue;

int step;

int x;

length = x2 - x1 + 1;

if (length > 0)

{

numcolors = lastcolor - firstcolor + 1;

colorvalue = firstcolor << 8;

step = ((long)numcolors << 8) / (long)length;

for (x = x1; x <= x2; x++)

{

drawpixel (x, y, colorvalue >> 8);

colorvalue += step;

}

}

}

x1 is the left coordinate of the line, with firstcolor being the color

of this point.

x2 is the right coordinate of the line, with lastcolor being the color

of this point.

y is the y coordinate of the horizontal line (you only need one).

drawpixel is a simple function which sets a single pixel to a color.

It is defined as:

void drawpixel (int x, int y, unsigned char col)

{

abuf [y * 320 + x] = col;

}

The above code is demonstrated in gshade1.c.

6.0 - Optimization Number 1

---------------------------

Calling drawpixel for each pixel is not very efficient.  We know the

pixels are one after the other, so it is useless to multiply the y

coordinate by 320 every time when we can just move over one pixel.

The following code shows how the drawpixel code has been simplified and

put directly into the shadedline routine.

void shadedline (int x1, int firstcolor, int x2, int lastcolor, int y)

{

int length;

int numcolors;

int colorvalue;

int step;

int x;

unsigned char far * dest;   /* Ptr to the screen */

length = x2 - x1 + 1;

if (length > 0)

{

numcolors = lastcolor - firstcolor + 1;

colorvalue = firstcolor << 8;

step = ((long)numcolors << 8) / (long)length;

dest = abuf + y * 320 + x1;

/* Make a pointer to the first pixel */

for (x = x1; x <= x2; x++)

{

*dest++ = colorvalue >> 8;

/* Draw the pixel and move to the next location in memory */

colorvalue += step;

}

}

}

The above code is demonstrated in gshade2.c.

7.0 - Optimization Number 2 (ASM)

---------------------------------

The other bottleneck in the routine is the colorvalue being shifted

right by 8 for every pixel.  By using the assembly language registers

mentioned earlier, we can take the high byte of colorvalue without

shifting.

The code below shows how inline assembly is used to speed up the

routine:

void shadedline (int x1, int firstcolor, int x2, int lastcolor, int y)

{

int length;

int numcolors;

int colorvalue;

int step;

int x;

unsigned char far * dest;   /* Ptr to the screen */

length = x2 - x1 + 1;

if (length > 0)

{

numcolors = lastcolor - firstcolor + 1;

colorvalue = firstcolor << 8;

step = ((long)numcolors << 8) / (long)length;

dest = abuf + y * 320 + x1;

/* Make a pointer to the first pixel */

/* Begin assembly optimization */

if (length > 0)

{

asm {

mov cx, word ptr length         /* Set length */

les di, dest                    /* Set destination ptr */

mov ax, word ptr colorvalue     /* Set color */

}

;

asm {

mov es:di, ah                   /* Move color to screen */

add ax, word ptr step           /* Add to color */

inc di                          /* Move to next pixel */

dec cx                          /* Decrease length */

jnz shadedlineloop              /* Repeat for all pixels */

}

}

}

}

The above code is demonstrated in gshade3.c.

8.0 - Combining The Shaded Line and Polygon Routines

----------------------------------------------------

The next question you may be asking is, "How do I know what colors to

use at the endpoints when drawing a polygon?".  In order to do this, we

have to modify our polygon scan conversion routines I developed in

tutorial #1.

The point structure is defined as:

typedef struct

{

int x,y;

} point;

Since each vertex now has a color associated with it, we will add another

variable to this structure, called col.  The point structure becomes the

gpoint structure, which looks like this:

typedef struct

{

int x,y;

unsigned char col;

} gpoint;

When we converted the polygon into a list of x coordinates, we stored them

into two arrays, startx and endx.  Now we also need to store the color

at both of these coordinates.

Let's make two new arrays:

int startcol[200];

int endcol[200];

When the list is created, we will have 2 x coordinates and a color value

associated with each of them.  This is all the information we need to call

The polyline routine becomes the gpolyline routine, which also calculates

the colors at the ends of each horizontal line.  To do this, we use fixed

point math, similar to the way we calculated the colors along the length

of the line.  This time we are adding the step value to the color

for every pixel we move down, instead of across.

void gpolyline (int x1, int y1, int col1, int x2, int y2, int col2)

/* Calculates the coordinates of a line given two

vertices (x1,y1) with color col1, and (x2,y2) with color col2.

We will use fixed point math to speed things up.

The x coordinate is multiplied by 256 and for each row,

a constant m is added to x.  This is a simplified version

of a line algorithm because we only have to store 1 x coordinate

for every y coordinate.

The color value is increase by a step value based on the

number of colors between the vertices and the distance between the

y coordinates.

*/

{

int tmp,y;

long x,m;

long col, colstep; /* First color, and the step value */

if (y2 != y1)      /* This isn't a horizontal line */

{

if (y2 < y1)     /* Make sure y2 is greater than y1 */

{

tmp = y1;       /* Swap the y coordinate */

y1 = y2;

y2 = tmp;

tmp = x1;       /* Swap the corresponding x coordinates */

x1 = x2;

x2 = tmp;

tmp = col1;     /* Swap the corresponding color values */

col1 = col2;

col2 = tmp;

}

x = (long)x1<<8;   /* Multiply be 256 */

m = ((long)(x2 - x1)<<8) / ((long)(y2 - y1));

/* m is the fractional amount to add to the x coordinate every row.

m is equal to (delta x) / (delta y).  In other words, the x coordinate

has to change by (x2 - x1) columns in (y2 - y1) rows. */

col = (long)col1 << 8;  /* Initial color in 8.8 fixed point format */

colstep = ((long)(col2 - col1) << 8) / ((long)(y2 - y1));

/* Calculate the color step value similar to the method in the

shadedline routine, only we're dividing by the delta y value. */

x += m; /* We ALWAYS skip the first point in every line. This is done */

y1++; /* because we do not want to store the point where two lines

meet, twice.  This would result in a single point being drawn. */

for (y = y1; y <= y2; y++) /* Go through each row */

{

if ((y >= 0) & (y < 200)) /* If the coordinate is on the screen */

if (startx[y] == -16000) /* Store the first coordinate */

{

startx[y] = x>>8;

startcol[y] = col >> 8;  /* store the color */

}

else

{

endx[y] = x>>8;        /* Store the last coordinate */

endcol[y] = col >> 8;

}

x += m;                   /* Add our constant to x */

col += colstep;

}

}

}

The fillpoly routine becomes the shadedpoly routine, which calls gpolyline

with the correct coordinates and color of each vertex, and finally the

void shadedpoly (gpoint *vertexlist, int numvertex)

/* Draws a shaded polygon given an array of vertices. */

{

int i;

gpoint *curpt,*nextpt;

/* Two pointers to a vertex. These are used to connect to vertices

together in when calling the gpolyline routine. */

curpt = vertexlist;      /* Set to the first vertex in the array */

nextpt = vertexlist + 1; /* and to the second vertex */

for (i = 0; i < 200; i++)

{

startx[i] = -16000;     /* Set up our impossible values */

endx[i] = -16000;

}

for (i = 1; i < numvertex; i++)

{

gpolyline (curpt->x,  curpt->y,  curpt->col,

nextpt->x, nextpt->y, nextpt->col);

/* Calculate the edge of this line. */

curpt += 1;  /* Go to the next line */

nextpt += 1;

}

nextpt = vertexlist;  /* Now close the polygon by doing a line between

the first and last vertex. */

gpolyline (curpt->x,  curpt->y,  curpt->col,

nextpt->x, nextpt->y, nextpt->col);

for (i = 0; i < 200; i++)   /* Now draw the horizontal line list */

if (startx[i] != -16000)  /* Indicates there is a line on this row */

{

if (endx[i] == -16000)

endx[i] = startx[i]; /* In case there was only one

point found on this row */

shadedline (startx[i], startcol[i], endx[i], endcol[i], i);

/* Draw a shaded line between the two x coordinates, on the row i. */

}

}

9.0 - What About Clipping?

--------------------------

So far we assumed the x coordinates of the shaded line would fall between

0 and 319 inclusively.  What happens if one of the x coordinates does not?

The line will wrap around to the other side of the screen.  You can

try this with any of the first 4 example programs.  It will probably cause

the system to crash since you are able to write to memory outside the

video display memory.

We have already clipped the y coordinate in the shadedpoly routine, so we

do not have to worry about that.

There are two possible cases that need clipping:

1. The left edge is less than 0

2. The right edge is greater than 319

The second case is easy to solve, since you can just decrease the length

of the line.  In other words, chop off the pixels past 319.   Note that

you should clip the line AFTER you calculate the step value since

changing the length will change the step value as well.

The code for clipping the right side would look something like this:

if (x2 > 319)    /* Set right coordinate to right clipping coordinate */

x2 = 319;

No other math is required.

The first case is a tricky one.  We cannot simply set x1 to 0, since the

first color would be wrong.  We have to increase the colorvalue to skip

over the pixels past the left edge.  We know that for each pixel the

colorvalue is increased by the step value, so we can multiply the

step value by the number of pixels past the left edge and add the

result to the colorvalue.  This will advance the color to the correct

value.

The code for clipping the right edge would look like this:

if (x1 < 0)                    /* Clip the left edge */

{

dist = 0 - x1;               /* Find number of pixels to be clipped */

colorvalue += dist * step;

/* Add dist color steps onto the starting value */

x1 = 0;

/* Set left coordinate to the left clippin coordinate*/

}

After the clipping is performed, the length of the line should be

recalculated.  The shadedline routine now looks like this:

void shadedline (int x1, int firstcolor, int x2, int lastcolor, int y)

{

int length;

int numcolors;

int colorvalue;

int step;

int x;

unsigned char far * dest;   /* Ptr to the screen */

int dist;

length = x2 - x1 + 1;

if (length > 0)

{

numcolors = lastcolor - firstcolor + 1;

colorvalue = firstcolor << 8;

step = ((long)numcolors << 8) / (long)length;

if (x2 > 319)    /* Set right coordinate to right clipping coordinate */

x2 = 319;

if (x1 < 0)                   /* Clip the left edge */

{

dist = 0 - x1;              /* Find number of pixels to be clipped */

colorvalue += dist * step;

/* Add dist color steps onto the starting value */

x1 = 0;

/* Set left coordinate to the left clippin coordinate*/

}

dest = abuf + y * 320 + x1;

/* Make a pointer to the first pixel */

length = x2 - x1 + 1;

/* Begin assembly optimization */

if (length > 0)

{

asm {

mov cx, word ptr length         /* Set length */

les di, dest                    /* Set destination ptr */

mov ax, word ptr colorvalue     /* Set color */

}

;

asm {

mov es:di, ah                   /* Move color to screen */

add ax, word ptr step           /* Add to color */

inc di                          /* Move to next pixel */

dec cx                          /* Decrease length */

jnz shadedlineloop              /* Repeat for all pixels */

}

}

}

}

10.0 - Other Issues

-------------------

The example programs included use the default palette.  This does not

produce a very nicely shaded polygon.  You should define your palette with

shades of colors. For example, colors 0 to 63 may contain shades of red,

while colors 64 to 127 contain shades of blue.  The more shades of colors

you use, the more realistic the shading will look, and less banding will

occur.  Banding occurs when you see distinct edges along each color in the

polygon.  This is caused by the colors being too different.

Gouraud shading also involves calculating the normal of the polygon and

comparing it with the direction of the lightsource in order to find

realistic values of colors at each vertex.  Since this deals with 3D

graphics, it is out of the scope of this tutorial.  You don't always need

to take this into account however.  You can base the color on the z value

of the vertex, or leave this out completely if you are strictly dealing

with 2D graphics.  As well, you may want to set the colors of the vertices

once and leave them the same throughout the rest of the program.

I hope you enjoyed this tutorial.  The next topic is texture mapping, which

is only a small change on the code presented here (believe it or not!).