Published Dec 19, 2019
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The simplest code that draws a line segment between (x0, y0) and (x1, y1)
points.
void line(int x0, int y0, int x1, int y1, TGAImage &image, TGAColor color){
for(float t = .0; t < 1.; t += .01){
int x = x0 + (x1 - x0)*t;
int y = y0 + (y1 - y0)*t;
image.set(x, y, color)
}
}
The idea here is to use the difference in x and y coordinate for two points as the step value, and change it step by step.
The problem with previous code (besides its inefficiency) is the choice of the constant, which I took equal to .01.
We can easily find the necessary step: it’s the number of pixels to be drawn.
void line(int x0, int y0, int x1, int y1, TGAImage &image, TGAColor color){
for( int x = x0; x < x1; x++){
float t = (x - x0) / (float)(x1 - x0);
int y = y0 + t*(y1 - y0);
image.set(x, y, color);
}
}
We fix the missing red line by swapping the points so x0 is always lower than x1.
There are holes in one of the line segments due to the fact that its height is greater than the width.
void line(int x0, int y0, int x1, int y1, TGAImage &image, TGAColor color){
bool steep = false;
// if line is steep, we transpose the image
if (std::abs(x0 - x1) < std::abs(y0 - y1)){
std::swap(x0, y0);
std::swap(x1, y1);
steep = true;
}
if (x0 > x1){ // make it left-to-right
std::swap(x0, x1);
std::swap(y0, y1);
}
for (int x = x0; x < x1; x++){
float t = (x - x0)/(float)(x1 - x0);
int y = y0 + t*(y1 - y0);
if(steep){
image.set(y, x, color); // if transposed, de-transpose
} else {
image.set(x, y, color);
}
}
}
We should note that each division has the same divisor. Let’s take it out of the loop. The error variable gives us the distance to the best straight line from our current (x, y) pixel. Each time error is greater than one pixel,we increase (or decrease) y by one, and decrease the error by one as well.
void line(int x0, int y0, int x1, int y1, TGAImage &image, TGAColor color){
bool steep = false;
if(std::abs(x0 - x1) < std::abs(y0 - y1)){
std::swap(x0, y0);
std::swap(x1, y1);
steep = true;
}
if (x0 > x1){
std::swap(x0, x1);
std::swap(y0, y1);
}
int dx = x1 - x0;
int dy = y1 - y0;
float derror = std::abs(dy/float(dx));
float error = 0;
int y = y0;
for (int x = x0; x < x1; x++){
if (steep){
image.set(y, x, color);
} else {
image.set(x, y, color);
}
error += derror;
if (error > 0.5){
y += (y1 > y0 ? 1 : -1);
error -= 1.;
}
}
}
Why do we need floating points? The only reason is one division by dx and comparison with .5 in the loop body. We can get rid of the floating point by replacing the error variable with another one. Let’s call it error2, and assume it is equal to errordx2.
void line(int x0, int y0, int x1, int y1, TGAImage &image, TGAColor color){
bool steep = false;
if(std::abs(x0 - x1) < std::abs(y0 - y1)){
std::swap(x0, y0);
std::swap(x1, y1);
steep = true;
}
if (x0 > x1){
std::swap(x0, x1);
std::swap(y0, y1);
}
int dx = x1 - x0;
int dy = y1 - y0;
int derror2 = std::abs(dy)*2
int error2 = 0;
int y = y0;
for(int x = x0; x <= x1; x++){
if(steep){
image.set(x, y, color);
} else {
image.set(y, x, color);
}
}
error2 += derror2;
if(error2 > dx){
y += (y1 > y0 ? 1 : -1);
error2 -= dx*2;
}
}