#include <iostream>
#include "perspective.h"
#include "perspectivesandboxview.h"
PerspectiveSandBoxView::PerspectiveSandBoxView():
persp_p0 (new View::Point( Vector2(-1, -1) )),
persp_px (new View::Point( Vector2( 1, -1) )),
persp_py (new View::Point( Vector2(-1, 1) )),
persp_p1 (new View::Point( Vector2( 1, 1) )),
bounds_p0 (new View::Point( Vector2(-2, -2) )),
bounds_p1 (new View::Point( Vector2( 2, 2) ))
{
transform.scale(50, 50);
points.push_back(persp_p0);
points.push_back(persp_px);
points.push_back(persp_py);
points.push_back(persp_p1);
points.push_back(bounds_p0);
points.push_back(bounds_p1);
}
static Vector2 calc_optimal_resolution(
const Vector2 &ox,
const Vector2 &oy )
{
const Real a = ox.x * ox.x;
const Real b = ox.y * ox.y;
const Real c = oy.x * oy.x;
const Real d = oy.y * oy.y;
Real e = fabs(ox.x*oy.y - ox.y*oy.x);
if (e < real_precision_sqr)
return Vector2(); // paranoid check, e must be non-zero when matrix is invertible
e = 1.0/e;
const Real sum = a*d + b*c;
Vector2 scale;
if (2*a*b + real_precision_sqr >= sum) {
scale.x = sqrt(2*b)*e;
scale.y = sqrt(2*a)*e;
} else
if (2*c*d + real_precision_sqr >= sum) {
scale.x = sqrt(2*d)*e;
scale.y = sqrt(2*c)*e;
} else {
const Real dif = a*d - b*c;
scale.x = sqrt(dif/(a - c))*e;
scale.y = sqrt(dif/(d - b))*e;
}
return scale;
}
void PerspectiveSandBoxView::update_background(
const Matrix3 &matrix,
int width,
int height )
{
DataSurface surface(width, height);
for(int r = 0; r < height; ++r) {
for(int c = 0; c < width; ++c) {
Vector3 v = matrix*Vector3(c, r, 1);
if (v.z <= real_precision)
continue;
const Real k = 1/(v.z*v.z);
const Vector2 ox = Vector2( v.z*matrix.m00 - matrix.m02*v.x,
v.z*matrix.m10 - matrix.m12*v.x )*k;
const Vector2 oy = Vector2( v.z*matrix.m01 - matrix.m02*v.y,
v.z*matrix.m11 - matrix.m12*v.y )*k;
const Vector2 resolution = calc_optimal_resolution(ox, oy)*100;
if (resolution.x <= real_precision || resolution.y <= real_precision)
continue;
const int lx = (int)round(log2(resolution.x));
const int ly = (int)round(log2(resolution.y));
Color color;
color.r = lx < 0 ? lx%2 + 1 : lx%2;
color.g = 0;
color.b = ly < 0 ? ly%2 + 1 : ly%2;
color.a = 1;
surface[r][c] = color;
}
}
background = surface.to_cairo_surface();
}
void
PerspectiveSandBoxView::draw_grid(
const Cairo::RefPtr<Cairo::Context> &context,
const Matrix &matrix,
const Color &color )
{
const int count = 100;
const int subcount = 10;
const Real ps = get_pixel_size();
for(int i = -count; i < count; ++i) {
for(int j = -count; j < count; ++j) {
Vector4 src(i/(Real)subcount, j/(Real)subcount, 0, 1);
Vector4 dst = matrix*src;
Real w = dst.w;
if (w > real_precision) {
Vector2 pos(dst.x/w, dst.y/w);
Real ka = clamp(1/w, 0, 1);
Real a = color.a*ka;
Real r = 4*ps;
if (i) r *= 0.5;
if (j) r *= 0.5;
if (i % 10) r *= 0.75;
if (j % 10) r *= 0.75;
context->set_source_rgba(color.r, color.g, color.b, a);
context->arc(pos.x, pos.y, r, 0, 2.0*M_PI);
context->fill();
}
}
}
}
void
PerspectiveSandBoxView::draw_line(
const Cairo::RefPtr<Cairo::Context> &context,
const Pair2 &bounds,
Real a,
Real b,
Real c,
const Color &color )
{
// equatation of line is a*x + b*y = c
int count = 0;
Vector2 points[4];
if (fabs(a) > real_precision) {
Real x0 = (c - bounds.p0.y*b)/a;
if ( x0 + real_precision >= bounds.p0.x
&& x0 - real_precision <= bounds.p1.x )
points[count++] = Vector2(x0, bounds.p0.y);
Real x1 = (c - bounds.p1.y*b)/a;
if ( x1 + real_precision >= bounds.p0.x
&& x1 - real_precision <= bounds.p1.x )
points[count++] = Vector2(x1, bounds.p1.y);
}
if (fabs(b) > real_precision) {
Real y0 = (c - bounds.p0.x*a)/b;
if ( y0 + real_precision >= bounds.p0.y
&& y0 - real_precision <= bounds.p1.y )
points[count++] = Vector2(bounds.p0.x, y0);
Real y1 = (c - bounds.p1.x*a)/b;
if ( y1 + real_precision >= bounds.p0.y
&& y1 - real_precision <= bounds.p1.y )
points[count++] = Vector2(bounds.p1.x, y1);
}
if (count >= 2) {
context->set_source_rgba(color.r, color.g, color.b, color.a);
context->move_to(points[0].x, points[0].y);
context->line_to(points[1].x, points[1].y);
context->stroke();
}
}
void
PerspectiveSandBoxView::draw_subdivisions(
const Cairo::RefPtr<Cairo::Context> &context,
const Matrix &matrix,
const Pair2 &bounds,
const Color &color )
{
const Real ps = get_pixel_size();
Vector4 a = matrix.row_x();
Vector4 b = matrix.row_y();
Vector4 c = matrix.row_w();
// calc coefficient for equatation of "horizontal" line: A*x + B*y = C + D/w
// equatation of line of horizon is: A*x + B*y = C
Real A = a.y*b.w - a.w*b.y;
Real B = a.w*b.x - a.x*b.w;
Real C = a.y*b.x - a.x*b.y;
Real D = a.w*(b.x*c.y - b.y*c.x) + b.w*(a.y*c.x - a.x*c.y) - C*c.w;
if (D < 0) {
A = -A;
B = -B;
C = -C;
D = -D;
}
Real hd = ps*sqrt(A*A + B*B);
if (hd <= real_precision)
return; // orthogonal projection - no prespective - no subdiviosions
hd = D/hd;
Real horizonw = hd;
Real horizonw2 = hd/4;
Real maxw = -INFINITY, minw = INFINITY;
Vector2 corners[] = {
Vector2(bounds.p0.x, bounds.p0.y),
Vector2(bounds.p1.x, bounds.p0.y),
Vector2(bounds.p1.x, bounds.p1.y),
Vector2(bounds.p0.x, bounds.p1.y) };
for(int i = 0; i < 4; ++i) {
Real w = A*corners[i].x + B*corners[i].y - C;
if (fabs(w) > real_precision) {
w = D/w;
if (w < 0 || w > horizonw) w = horizonw;
if (minw > w) minw = w;
if (maxw < w) maxw = w;
}
}
if (minw >= maxw - real_precision)
return; // all bounds too thin
Real maxw2 = maxw < horizonw2 ? maxw : horizonw2;
// draw limits
Color limits_color = color;
limits_color.a *= 0.5;
draw_line(context, get_bounds(), A, B, C + D/minw, limits_color);
draw_line(context, get_bounds(), A, B, C + D/maxw, limits_color);
// split
int minlog = (int)ceil (log2(minw ) + real_precision);
int maxlog = (int)floor(log2(maxw2) - real_precision);
for(int i = minlog; i <= maxlog; ++i)
draw_line(context, bounds, A, B, C + D/exp2(i), color);
}
void
PerspectiveSandBoxView::on_draw_view(const Cairo::RefPtr<Cairo::Context> &context) {
context->save();
const Real ps = get_pixel_size();
context->set_line_width(ps);
Vector2 p0 = persp_p0->position;
Vector2 px = persp_px->position;
Vector2 py = persp_py->position;
Vector2 p1 = persp_p1->position;
Pair2 bounds(bounds_p0->position, bounds_p1->position);
// perspective matrix
Matrix matrix;
{
Vector2 A = px - p1;
Vector2 B = py - p1;
Vector2 C = p0 + p1 - px - py;
Real cw = A.y*B.x - A.x*B.y;
Real aw = B.x*C.y - B.y*C.x;
Real bw = A.y*C.x - A.x*C.y;
if (cw < 0) {
aw = -aw;
bw = -bw;
cw = -cw;
}
Vector2 c = p0*cw;
Vector2 a = px*(cw + aw) - c;
Vector2 b = py*(cw + bw) - c;
matrix.row_x() = Vector4(a, 0, aw);
matrix.row_y() = Vector4(b, 0, bw);
matrix.row_w() = Vector4(c, 0, cw);
}
{ // update background
Matrix4 m4 = transform_to_pixels()*matrix;
Matrix3 m3(
Vector3( m4.m00, m4.m01, m4.m03 ),
Vector3( m4.m10, m4.m11, m4.m13 ),
Vector3( m4.m30, m4.m31, m4.m33 ) );
Matrix3 back_matrix = Perspective::normalize_matrix( m3.inverted() );
update_background(back_matrix, get_width(), get_height());
}
if (background) {
context->save();
context->transform(transform_from_pixels().to_cairo());
context->set_source(background, 0, 0);
context->paint();
context->restore();
}
draw_grid(context, matrix, Color(0, 1, 0, 1));
draw_subdivisions(context, matrix, bounds, Color(0, 0, 1, 1));
// draw frames
context->set_source_rgba(0, 0, 1, 0.75);
context->move_to(p0.x, p0.y);
context->line_to(px.x, px.y);
context->line_to(p1.x, p1.y);
context->line_to(py.x, py.y);
context->close_path();
context->stroke();
context->move_to(bounds.p0.x, bounds.p0.y);
context->line_to(bounds.p1.x, bounds.p0.y);
context->line_to(bounds.p1.x, bounds.p1.y);
context->line_to(bounds.p0.x, bounds.p1.y);
context->close_path();
context->stroke();
context->restore();
}