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rotate-me-fast
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Draw rotated outlines. 

There is a bug for rotation = pi / 2
master
Fabien Freling 2014-06-19 00:05:49 +02:00
parent 4bf69e8204
commit 8a17f7b8d8
3 changed files with 145 additions and 98 deletions
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2
Makefile
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@ -1,5 +1,5 @@
CXX = clang++
CXXFLAGS = -std=c++11 -W -Wall -Werror -O3
CXXFLAGS = -std=c++11 -W -Wall -O3 #-Werror
BUILD_DIR=/tmp
all: rotation.cpp

1
TODO.md
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@ -0,0 +1 @@
[ ] Quaternions

240
rotation.cpp
View File

@ -215,13 +215,21 @@ struct Image {
void draw_line(Image& img, unsigned int x1, unsigned int y1, unsigned int x2, unsigned int y2)
{
assert(x1 < x2);
double const slope = (double) (y2 - y1) / (double) (x2 - x1);
if (x1 > x2)
{
swap(x1, x2);
swap(y1, y2);
}
double const slope = ((double) y2 - y1) / ((double) x2 - x1);
cout << "draw slope = " << slope << endl;
unsigned int previous_y = y1;
for (unsigned int i = x1; i <= x2; ++i)
{
unsigned int y = slope * (i - x1) + y1;
img.set_pixel(i, y, 255, 0, 0); // set line to red
int inc = slope > 0 ? 1 : -1;
for (unsigned int runner = previous_y; runner != y; runner+= inc)
img.set_pixel(i, runner, 255, 0, 0); // set line to red
previous_y = y;
}
}
@ -230,24 +238,6 @@ void draw_line(Image& img, Point const& p1, Point const& p2)
draw_line(img, p1.x, p1.y, p2.x, p2.y);
}
Point rotate(Image const& img, Point const& src, double radian, double const ratio)
{
cout << "rotate (" << src.x << ", " << src.y << ") x " << radian << endl;
double x = src.x - (img.width / 2.0f);
x *= ratio;
// double y = - src.y + (src.height / 2.0f);
// y *= ratio;
double const angle_value = acos(x) + radian;
double const cos_x = cos(angle_value);
double const sin_x = sin(angle_value);
unsigned int const new_x = ceil(cos_x / ratio);
unsigned int const new_y = ceil(sin_x / ratio);
cout << " = (" << new_x << ", " << new_y << ")" << endl;
return Point(new_x, new_y);
}
//
//
@ -256,11 +246,8 @@ Point rotate(Image const& img, Point const& src, double radian, double const rat
double convert_radian(Image const& img, Point const& p, double const ratio)
{
cout << "X: " << p.x << " - " << img.width / 2.0f << endl;
cout << "Y: " << - (int) p.y << " + " << img.height / 2.0f << endl;
double const centered_x = p.x - (img.width / 2.0f);
double const centered_y = (- (int) p.y) + (img.height / 2.0f);
cout << "centered point (" << centered_x << ", " << centered_y << ")" << endl;
double const cos_value = centered_x * ratio;
double const sin_value = centered_y * ratio;
double angle = acos(cos_value);
@ -272,33 +259,20 @@ double convert_radian(Image const& img, Point const& p, double const ratio)
APoint convert_abs_coord(double const angle, double const ratio)
{
cout << "Angle: " << angle << endl;
cout << "cos: " << cos(angle) << endl;
cout << "sin: " << sin(angle) << endl;
APoint tmp((int) ceil(cos(angle) / ratio), (int) ceil(sin(angle) / ratio));
cout << "point: " << tmp << endl;
return APoint((int) ceil(cos(angle) / ratio), (int) ceil(sin(angle) / ratio));
}
Point convert_img_coord(Image const& img, APoint const& p)
{
cout << "image: " << img.width << " x " << img.height << endl;
cout << "p: " << p << endl;
cout << "h / 2: " << img.height / 2.0f << endl;
return Point(p.x + img.width / 2.0f, - p.y + img.height / 2.0f);
}
double compute_ratio(Image const& img)
{
cout << "Compute ratio" << endl;
unsigned int const nb_points = img.width * img.height;
cout << " " << nb_points << " points" << endl;
double const square_side = sqrt(nb_points) - 1;
cout << " square side: " << square_side << endl;
double const half_side = square_side / 2;
cout << " half side: " << half_side << endl;
unsigned int const trigo_length = (unsigned int) ceil(half_side * sqrt(2));
cout << " trigo length: " << trigo_length << endl;
return 1.0f / trigo_length;
}
@ -316,7 +290,7 @@ void compute_output_size(Image const& src, double const rotation, unsigned int&
int min_h = 0;
int max_h = 0;
cout << "Image dimensions: " << src.width << " x " << src.height << endl;
//cout << "Image dimensions: " << src.width << " x " << src.height << endl;
Point p(0, 0);
double angle = convert_radian(src, p, ratio);
APoint tl = convert_abs_coord(angle + rotation, ratio);
@ -324,7 +298,7 @@ void compute_output_size(Image const& src, double const rotation, unsigned int&
max_w = max(max_w, tl.x);
min_h = min(min_h, tl.y);
max_h = max(max_h, tl.y);
cout << "Rotated " << p << " (" << angle << ") = " << tl << "(" << angle + rotation << ")" << endl << endl;
//cout << "Rotated " << p << " (" << angle << ") = " << tl << "(" << angle + rotation << ")" << endl << endl;
p = Point(src.width - 1, 0);
angle = convert_radian(src, p, ratio);
@ -333,7 +307,7 @@ void compute_output_size(Image const& src, double const rotation, unsigned int&
max_w = max(max_w, tr.x);
min_h = min(min_h, tr.y);
max_h = max(max_h, tr.y);
cout << "Rotated " << p << " (" << angle << ") = " << tr << "(" << angle + rotation << ")" << endl << endl;
//cout << "Rotated " << p << " (" << angle << ") = " << tr << "(" << angle + rotation << ")" << endl << endl;
p = Point(0, src.height - 1);
angle = convert_radian(src, p, ratio);
@ -342,7 +316,7 @@ void compute_output_size(Image const& src, double const rotation, unsigned int&
max_w = max(max_w, bl.x);
min_h = min(min_h, bl.y);
max_h = max(max_h, bl.y);
cout << "Rotated " << p << " (" << angle << ") = " << bl << "(" << angle + rotation << ")" << endl << endl;
//cout << "Rotated " << p << " (" << angle << ") = " << bl << "(" << angle + rotation << ")" << endl << endl;
p = Point(src.width - 1, src.height - 1);
angle = convert_radian(src, p, ratio);
@ -351,12 +325,39 @@ void compute_output_size(Image const& src, double const rotation, unsigned int&
max_w = max(max_w, br.x);
min_h = min(min_h, br.y);
max_h = max(max_h, br.y);
cout << "Rotated " << p << " (" << angle << ") = " << br << "(" << angle + rotation << ")" << endl << endl;
//cout << "Rotated " << p << " (" << angle << ") = " << br << "(" << angle + rotation << ")" << endl << endl;
width = max_w - min_w + 1;
height = max_h - min_h + 1;
}
//
//
// Rotation
//
Point rotate(Image const& src, Point const& p, double const ratio, double const rotation, Image const& rotated)
{
double angle = convert_radian(src, p, ratio);
APoint a_point = convert_abs_coord(angle + rotation, ratio);
return convert_img_coord(rotated, a_point);
}
Image rotate(Image const& src, double angle)
{
// FIXME
Image rot(0, 0);
cout << angle << src.width << endl; // to remove warnings
return rot;
}
//
//
// Check
//
bool check_trigo()
{
Image square(500, 500);
@ -397,71 +398,114 @@ bool check_trigo()
compute_output_size(square, rotation, w, h);
// failed check: is precision an issue?
// if (!fequal(w, square.width * sqrt(2), sigma)
// || !fequal(h, square.height * sqrt(2), sigma))
// {
// cerr << "Invalid rotated image dimensions " << w << " x " << h << endl;
// cerr << " expected " << (int) ceil(square.width * sqrt(2)) << " x " << (int) ceil(square.height * sqrt(2)) << endl;
// return false;
// }
Image rotated(w, h);
APoint const a_p45 = convert_abs_coord(angle + rotation, ratio);
Point const p45 = convert_img_coord(rotated, a_p45);
if (abs((float) (-1) - p45.x) > sigma)
if (false)
{
cerr << "Rotation origin by 45 degrees:" << endl;
cerr << "Invalid x value: " << p45.x << " != " << -1 << endl;
cerr << "Absolute point: (" << a_p45.x << ", " << a_p45.y << ")" << endl;
return false;
}
if (abs(0.0 - p45.y) > sigma)
{
cerr << "Rotation origin by 45 degrees:" << endl;
cerr << "Invalid y value: " << p45.y << " != " << 0 << endl;
return false;
if (!fequal(w, square.width * sqrt(2), sigma)
|| !fequal(h, square.height * sqrt(2), sigma))
{
cerr << "Invalid rotated image dimensions " << w << " x " << h << endl;
cerr << " expected " << (int) ceil(square.width * sqrt(2)) << " x " << (int) ceil(square.height * sqrt(2)) << endl;
return false;
}
Image rotated(w, h);
APoint const a_p45 = convert_abs_coord(angle + rotation, ratio);
Point const p45 = convert_img_coord(rotated, a_p45);
if (abs((float) (0) - p45.x) > sigma)
{
cerr << "Rotation origin by 45 degrees:" << endl;
cerr << " invalid x value: " << p45.x << " != " << 0 << endl;
cerr << " absolute point: " << a_p45 << endl;
cerr << " relative point: " << p45 << endl;
return false;
}
if (abs(0.0 - p45.y) > sigma)
{
cerr << "Rotation origin by 45 degrees:" << endl;
cerr << "Invalid y value: " << p45.y << " != " << 0 << endl;
return false;
}
}
return true;
}
//
//
// Rotation
//
Image rotate(Image const& src, double angle)
void check_lines()
{
unsigned int const nb_points = src.width * src.height;
double const square_side = sqrt(nb_points);
double const half_side = square_side / 2;
unsigned int const trigo_length = (unsigned int) ceil(half_side * sqrt(2));
double const ratio = 1.0f / trigo_length;
Image const square(500, 500);
double const ratio = compute_ratio(square);
unsigned int w = 0;
unsigned int h = 0;
{
double const rotation = M_PI / 8; // 22 degrees
compute_output_size(square, rotation, w, h);
Image rotated(w, h);
// top left
double const cos_value = - (src.width / 2.0f) * ratio;
// double const sin_value = (src.height / 2.0f) * ratio;
double const angle_value = acos(cos_value);
cout << "top left angle: " << angle_value << endl;
Point tl = rotate(square, Point(0, 0), ratio, rotation, rotated);
Point tr = rotate(square, Point(square.width - 1, 0), ratio, rotation, rotated);
Point bl = rotate(square, Point(0, square.height - 1), ratio, rotation, rotated);
Point br = rotate(square, Point(square.width - 1, square.height - 1), ratio, rotation, rotated);
double const radian = (angle / 360.0f) * (2 * M_PI);
draw_line(rotated, tl, tr);
draw_line(rotated, tr, br);
draw_line(rotated, br, bl);
draw_line(rotated, bl, tl);
rotated.save("check_lines_01.ppm");
}
{
double const rotation = M_PI / 6; // 33 degrees
compute_output_size(square, rotation, w, h);
Image rotated(w, h);
// FIXME
Image rot(trigo_length, trigo_length);
Point tl = rotate(src, Point(0, 0), radian, ratio);
Point tr = rotate(src, Point(src.width - 1, 0), radian, ratio);
draw_line(rot, tl, tr);
// draw_line(rot, 0, 0, rot.width - 1, 0);
// draw_line(rot, 0, rot.height - 1, rot.width - 1, rot.height - 1);
// draw_line(rot, 0, 0, rot.width - 1, rot.height - 1);
// rot.set_pixel(rot.width - 1, rot.height - 1, 0, 255, 0);
// draw_line(rot, 0, 0, 0, rot.height - 1);
// draw_line(rot, rot.width - 1, 0, rot.width - 1, rot.height - 1);
return rot;
Point tl = rotate(square, Point(0, 0), ratio, rotation, rotated);
Point tr = rotate(square, Point(square.width - 1, 0), ratio, rotation, rotated);
Point bl = rotate(square, Point(0, square.height - 1), ratio, rotation, rotated);
Point br = rotate(square, Point(square.width - 1, square.height - 1), ratio, rotation, rotated);
draw_line(rotated, tl, tr);
draw_line(rotated, tr, br);
draw_line(rotated, br, bl);
draw_line(rotated, bl, tl);
rotated.save("check_lines_02.ppm");
}
{
double const rotation = M_PI / 4; // 45 degrees
compute_output_size(square, rotation, w, h);
Image rotated(w, h);
Point tl = rotate(square, Point(0, 0), ratio, rotation, rotated);
Point tr = rotate(square, Point(square.width - 1, 0), ratio, rotation, rotated);
Point bl = rotate(square, Point(0, square.height - 1), ratio, rotation, rotated);
Point br = rotate(square, Point(square.width - 1, square.height - 1), ratio, rotation, rotated);
draw_line(rotated, tl, tr);
draw_line(rotated, tr, br);
draw_line(rotated, br, bl);
draw_line(rotated, bl, tl);
rotated.save("check_lines_03.ppm");
}
{
double const rotation = M_PI / 2; // 90 degrees
compute_output_size(square, rotation, w, h);
Image rotated(w, h);
Point tl = rotate(square, Point(0, 0), ratio, rotation, rotated);
Point tr = rotate(square, Point(square.width - 1, 0), ratio, rotation, rotated);
Point bl = rotate(square, Point(0, square.height - 1), ratio, rotation, rotated);
Point br = rotate(square, Point(square.width - 1, square.height - 1), ratio, rotation, rotated);
draw_line(rotated, tl, tr);
draw_line(rotated, tr, br);
draw_line(rotated, br, bl);
draw_line(rotated, bl, tl);
rotated.save("check_lines_04.ppm");
}
}
@ -475,6 +519,8 @@ int main()
if (!check_trigo())
return 1;
check_lines();
return 0;
Image img("img/luigi.ppm");