dlib C++ Library - canvas_drawing.h

    // Copyright (C) 2005  Davis E. King (davis@dlib.net), and Nils Labugt
    // License: Boost Software License   See LICENSE.txt for the full license.

    #ifndef DLIB_GUI_CANVAS_DRAWINg_
    #define DLIB_GUI_CANVAS_DRAWINg_

    #include "canvas_drawing_abstract.h"
    #include "../gui_core.h"
    #include "../algs.h"
    #include "../array2d.h"
    #include "../pixel.h"
    #include "../image_transforms/assign_image.h"
    #include "../geometry.h"
    #include <cmath>

    namespace dlib
    {

    // ----------------------------------------------------------------------------------------

        template <typename pixel_type>
        void draw_line (
            const canvas& c,
            const point& p1,
            const point& p2,
            const pixel_type& pixel,
            const rectangle& area = rectangle(std::numeric_limits<long>::min(), std::numeric_limits<long>::min(),
                                              std::numeric_limits<long>::max(), std::numeric_limits<long>::max())
        )
        {
            rectangle valid_area(c.intersect(area));
            long x1 = p1.x();
            long y1 = p1.y();
            long x2 = p2.x();
            long y2 = p2.y();
            if (x1 == x2)
            {
                // if the x coordinate is inside the canvas's area
                if (x1 <= valid_area.right() && x1 >= valid_area.left())
                {
                    // make sure y1 comes before y2
                    if (y1 > y2)
                        swap(y1,y2);

                    y1 = std::max(y1,valid_area.top());
                    y2 = std::min(y2,valid_area.bottom());
                    // this is a vertical line
                    for (long y = y1; y <= y2; ++y)
                    {
                        assign_pixel(c[y-c.top()][x1-c.left()], pixel);
                    }
                }
            }
            else if (y1 == y2)
            {
                // if the y coordinate is inside the canvas's area
                if (y1 <= valid_area.bottom() && y1 >= valid_area.top())
                {
                    // make sure x1 comes before x2
                    if (x1 > x2)
                        swap(x1,x2);

                    x1 = std::max(x1,valid_area.left());
                    x2 = std::min(x2,valid_area.right());
                    // this is a horizontal line
                    for (long x = x1; x <= x2; ++x)
                    {
                        assign_pixel(c[y1-c.top()][x-c.left()], pixel);
                    }
                }
            }
            else
            {
                rgb_alpha_pixel alpha_pixel;
                assign_pixel(alpha_pixel, pixel);
                const unsigned char max_alpha = alpha_pixel.alpha;

                const long rise = (((long)y2) - ((long)y1));
                const long run = (((long)x2) - ((long)x1));
                if (std::abs(rise) < std::abs(run))
                {
                    const double slope = ((double)rise)/run;

                    double first, last;

                    if (x1 > x2)
                    {
                        first = std::max(x2,valid_area.left());
                        last = std::min(x1,valid_area.right());
                    }
                    else
                    {
                        first = std::max(x1,valid_area.left());
                        last = std::min(x2,valid_area.right());
                    }

                    long y;
                    long x;
                    const double x1f = x1;
                    const double y1f = y1;
                    for (double i = first; i <= last; ++i)
                    {
                        const double dy = slope*(i-x1f) + y1f;
                        const double dx = i;

                        y = static_cast<long>(dy);
                        x = static_cast<long>(dx);

                        if (y >= valid_area.top() && y <= valid_area.bottom())
                        {
                            alpha_pixel.alpha = static_cast<unsigned char>((1.0-(dy-y))*max_alpha);
                            assign_pixel(c[y-c.top()][x-c.left()], alpha_pixel);
                        }
                        if (y+1 >= valid_area.top() && y+1 <= valid_area.bottom())
                        {
                            alpha_pixel.alpha = static_cast<unsigned char>((dy-y)*max_alpha);
                            assign_pixel(c[y+1-c.top()][x-c.left()], alpha_pixel);
                        }
                    }
                }
                else
                {
                    const double slope = ((double)run)/rise;

                    double first, last;

                    if (y1 > y2)
                    {
                        first = std::max(y2,valid_area.top());
                        last = std::min(y1,valid_area.bottom());
                    }
                    else
                    {
                        first = std::max(y1,valid_area.top());
                        last = std::min(y2,valid_area.bottom());
                    }

                    long x;
                    long y;
                    const double x1f = x1;
                    const double y1f = y1;
                    for (double i = first; i <= last; ++i)
                    {
                        const double dx = slope*(i-y1f) + x1f;
                        const double dy = i;

                        y = static_cast<long>(dy);
                        x = static_cast<long>(dx);

                        if (x >= valid_area.left() && x <= valid_area.right())
                        {
                            alpha_pixel.alpha = static_cast<unsigned char>((1.0-(dx-x))*max_alpha);
                            assign_pixel(c[y-c.top()][x-c.left()], alpha_pixel);
                        }
                        if (x+1 >= valid_area.left() && x+1 <= valid_area.right())
                        {
                            alpha_pixel.alpha = static_cast<unsigned char>((dx-x)*max_alpha);
                            assign_pixel(c[y-c.top()][x+1-c.left()], alpha_pixel);
                        }
                    }
                }
            }

        }
        inline void draw_line (
            const canvas& c,
            const point& p1,
            const point& p2
        ){ draw_line(c,p1,p2,0); }

    // ----------------------------------------------------------------------------------------

        void draw_sunken_rectangle (
            const canvas& c,
            const rectangle& border,
            unsigned char alpha = 255
        );

    // ----------------------------------------------------------------------------------------

        template <typename pixel_type>
        inline void draw_pixel (
            const canvas& c,
            const point& p,
            const pixel_type& pixel
        )
        {
            if (c.contains(p))
            {
                assign_pixel(c[p.y()-c.top()][p.x()-c.left()],pixel);
            }
        }

    // ----------------------------------------------------------------------------------------

        template <typename pixel_type>
        void draw_checkered (
            const canvas& c,
            const rectangle& a,
            const pixel_type& pixel1,
            const pixel_type& pixel2
        )
        {
            rectangle area = a.intersect(c);
            if (area.is_empty())
                return;

            for (long i = area.left(); i <= area.right(); ++i)
            {
                for (long j = area.top(); j <= area.bottom(); ++j)
                {
                    canvas::pixel& p = c[j - c.top()][i - c.left()];
                    if ((j&0x1) ^ (i&0x1))
                    {
                        assign_pixel(p,pixel1);
                    }
                    else
                    {
                        assign_pixel(p,pixel2);
                    }
                }
            }
        }

    // ----------------------------------------------------------------------------------------

        void draw_button_down (
            const canvas& c,
            const rectangle& btn,
            unsigned char alpha = 255
        );

    // ----------------------------------------------------------------------------------------

        void draw_button_up (
            const canvas& c,
            const rectangle& btn,
            unsigned char alpha = 255
        );

    // ----------------------------------------------------------------------------------------

        template <typename pixel_type>
        void draw_circle (
            const canvas& c,
            const point& center_point,
            double radius,
            const pixel_type& pixel,
            const rectangle& area = rectangle(std::numeric_limits<long>::min(), std::numeric_limits<long>::min(),
                                              std::numeric_limits<long>::max(), std::numeric_limits<long>::max())
        )
        {
            using std::sqrt;
            rectangle valid_area(c.intersect(area));
            const long x = center_point.x();
            const long y = center_point.y();
            if (radius > 1)
            {
                long first_x = std::lround(x - radius);
                long last_x = std::lround(x + radius);
                const double rs = radius*radius;

                // ensure that we only loop over the part of the x dimension that this
                // canvas contains.
                if (first_x < valid_area.left())
                    first_x = valid_area.left();
                if (last_x > valid_area.right())
                    last_x = valid_area.right();

                long top, bottom;

                top = std::lround(sqrt(std::max(rs - (first_x-x-0.5)*(first_x-x-0.5),0.0)));
                top += y;
                long last = top;

                // draw the left half of the circle
                long middle = std::min(x-1,last_x);
                for (long i = first_x; i <= middle; ++i)
                {
                    double a = i - x + 0.5;
                    // find the top of the arc
                    top = std::lround(sqrt(std::max(rs - a*a,0.0)));
                    top += y;
                    long temp = top;

                    while(top >= last)
                    {
                        bottom = y - top + y;
                        if (top >= valid_area.top() && top <= valid_area.bottom() )
                        {
                            assign_pixel(c[top-c.top()][i-c.left()],pixel);
                        }

                        if (bottom >= valid_area.top() && bottom <= valid_area.bottom() )
                        {
                            assign_pixel(c[bottom-c.top()][i-c.left()],pixel);
                        }
                        --top;
                    }

                    last = temp;
                }

                middle = std::max(x,first_x);
                top = std::lround(sqrt(std::max(rs - (last_x-x+0.5)*(last_x-x+0.5),0.0)));
                top += y;
                last = top;
                // draw the right half of the circle
                for (long i = last_x; i >= middle; --i)
                {
                    double a = i - x - 0.5;
                    // find the top of the arc
                    top = std::lround(sqrt(std::max(rs - a*a,0.0)));
                    top += y;
                    long temp = top;

                    while(top >= last)
                    {
                        bottom = y - top + y;
                        if (top >= valid_area.top() && top <= valid_area.bottom() )
                        {
                            assign_pixel(c[top-c.top()][i-c.left()],pixel);
                        }

                        if (bottom >= valid_area.top() && bottom <= valid_area.bottom() )
                        {
                            assign_pixel(c[bottom-c.top()][i-c.left()],pixel);
                        }
                        --top;
                    }

                    last = temp;
                }
            }
            else if (radius == 1 &&
                     x >= valid_area.left() && x <= valid_area.right() &&
                     y >= valid_area.top() && y <= valid_area.bottom() )
            {
                assign_pixel(c[y-c.top()][x-c.left()], pixel);
            }
        }
        inline void draw_circle (
            const canvas& c,
            const point& center_point,
            double radius
        ){ draw_circle(c, center_point, radius, 0); }

    // ----------------------------------------------------------------------------------------

        template <typename pixel_type>
        void draw_solid_circle (
            const canvas& c,
            const point& center_point,
            double radius,
            const pixel_type& pixel,
            const rectangle& area = rectangle(std::numeric_limits<long>::min(), std::numeric_limits<long>::min(),
                                              std::numeric_limits<long>::max(), std::numeric_limits<long>::max())
        )
        {
            using std::sqrt;
            rectangle valid_area(c.intersect(area));
            const long x = center_point.x();
            const long y = center_point.y();
            if (radius > 1)
            {
                long first_x = std::lround(x - radius);
                long last_x = std::lround(x + radius);
                const double rs = radius*radius;

                // ensure that we only loop over the part of the x dimension that this
                // canvas contains.
                if (first_x < valid_area.left())
                    first_x = valid_area.left();
                if (last_x > valid_area.right())
                    last_x = valid_area.right();

                long top, bottom;

                top = std::lround(sqrt(std::max(rs - (first_x-x-0.5)*(first_x-x-0.5),0.0)));
                top += y;
                long last = top;

                // draw the left half of the circle
                long middle = std::min(x-1,last_x);
                for (long i = first_x; i <= middle; ++i)
                {
                    double a = i - x + 0.5;
                    // find the top of the arc
                    top = std::lround(sqrt(std::max(rs - a*a,0.0)));
                    top += y;
                    long temp = top;

                    while(top >= last)
                    {
                        bottom = y - top + y;
                        draw_line(c, point(i,top),point(i,bottom),pixel,area);
                        --top;
                    }

                    last = temp;
                }

                middle = std::max(x,first_x);
                top = std::lround(sqrt(std::max(rs - (last_x-x+0.5)*(last_x-x+0.5),0.0)));
                top += y;
                last = top;
                // draw the right half of the circle
                for (long i = last_x; i >= middle; --i)
                {
                    double a = i - x - 0.5;
                    // find the top of the arc
                    top = std::lround(sqrt(std::max(rs - a*a,0.0)));
                    top += y;
                    long temp = top;

                    while(top >= last)
                    {
                        bottom = y - top + y;
                        draw_line(c, point(i,top),point(i,bottom),pixel,area);
                        --top;
                    }

                    last = temp;
                }
            }
            else if (radius == 1 &&
                     x >= valid_area.left() && x <= valid_area.right() &&
                     y >= valid_area.top() && y <= valid_area.bottom() )
            {
                assign_pixel(c[y-c.top()][x-c.left()], pixel);
            }
        }
        inline void draw_solid_circle (
            const canvas& c,
            const point& center_point,
            double radius
        ) { draw_solid_circle(c, center_point, radius, 0); }

    // ----------------------------------------------------------------------------------------

        template <typename pixel_type>
        void draw_solid_convex_polygon (
            const canvas& c,
            const polygon& poly,
            const pixel_type& pixel,
            const rectangle& area = rectangle(std::numeric_limits<long>::min(), std::numeric_limits<long>::min(),
                                              std::numeric_limits<long>::max(), std::numeric_limits<long>::max())
        )
        {
            using std::max;
            using std::min;
            const rectangle valid_area(c.intersect(area));

            const rectangle bounding_box = poly.get_rect();

            // Don't do anything if the polygon is totally outside the area we can draw in
            // right now.
            if (bounding_box.intersect(valid_area).is_empty())
                return;

            rgb_alpha_pixel alpha_pixel;
            assign_pixel(alpha_pixel, pixel);
            const unsigned char max_alpha = alpha_pixel.alpha;

            // we will only want to loop over the part of left_boundary that is part of the
            // valid_area.
            long top = max(valid_area.top(),bounding_box.top());
            long bottom = min(valid_area.bottom(),bounding_box.bottom());

            // Since we look at the adjacent rows of boundary information when doing the alpha
            // blending, we want to make sure we always have some boundary information unless
            // we are at the absolute edge of the polygon.
            const long top_offset = (top == bounding_box.top()) ? 0 : 1;
            const long bottom_offset = (bottom == bounding_box.bottom()) ? 0 : 1;
            if (top != bounding_box.top())
                top -= 1;
            if (bottom != bounding_box.bottom())
                bottom += 1;

            std::vector<double> left_boundary;
            std::vector<double> right_boundary;
            poly.get_left_and_right_bounds(top, bottom, left_boundary, right_boundary);

            // draw the polygon row by row
            for (unsigned long i = top_offset; i < left_boundary.size(); ++i)
            {
                long left_x = static_cast<long>(std::ceil(left_boundary[i]));
                long right_x = static_cast<long>(std::floor(right_boundary[i]));

                left_x = max(left_x, valid_area.left());
                right_x = min(right_x, valid_area.right());

                if (i < left_boundary.size()-bottom_offset)
                {
                    // draw the main body of the polygon
                    for (long x = left_x; x <= right_x; ++x)
                    {
                        const long y = i+top;
                        assign_pixel(c[y-c.top()][x-c.left()], pixel);
                    }
                }

                if (i == 0)
                    continue;

                // Now draw anti-aliased edges so they don't look all pixely.

                // Alpha blend the edges on the left side.
                double delta = left_boundary[i-1] - left_boundary[i];
                if (std::abs(delta) <= 1)
                {
                    if (std::floor(left_boundary[i]) != left_x)
                    {
                        const point p(static_cast<long>(std::floor(left_boundary[i])), i+top);
                        rgb_alpha_pixel temp = alpha_pixel;
                        temp.alpha = max_alpha-static_cast<unsigned char>((left_boundary[i]-p.x())*max_alpha);
                        if (valid_area.contains(p))
                            assign_pixel(c[p.y()-c.top()][p.x()-c.left()],temp);
                    }
                }
                else if (delta < 0)  // on the bottom side
                {
                    for (long x = static_cast<long>(std::ceil(left_boundary[i-1])); x < left_x; ++x)
                    {
                        const point p(x, i+top);
                        rgb_alpha_pixel temp = alpha_pixel;
                        temp.alpha = static_cast<unsigned char>((x-left_boundary[i-1])/std::abs(delta)*max_alpha);
                        if (valid_area.contains(p))
                            assign_pixel(c[p.y()-c.top()][p.x()-c.left()],temp);
                    }
                }
                else // on the top side
                {
                    const long old_left_x = static_cast<long>(std::ceil(left_boundary[i-1]));
                    for (long x = left_x; x < old_left_x; ++x)
                    {
                        const point p(x, i+top-1);
                        rgb_alpha_pixel temp = alpha_pixel;
                        temp.alpha = static_cast<unsigned char>((x-left_boundary[i])/delta*max_alpha);
                        if (valid_area.contains(p))
                            assign_pixel(c[p.y()-c.top()][p.x()-c.left()],temp);
                    }
                }

                // Alpha blend the edges on the right side
                delta = right_boundary[i-1] - right_boundary[i];
                if (std::abs(delta) <= 1)
                {
                    if (std::ceil(right_boundary[i]) != right_x)
                    {
                        const point p(static_cast<long>(std::ceil(right_boundary[i])), i+top);
                        rgb_alpha_pixel temp = alpha_pixel;
                        temp.alpha = max_alpha-static_cast<unsigned char>((p.x()-right_boundary[i])*max_alpha);
                        if (valid_area.contains(p))
                            assign_pixel(c[p.y()-c.top()][p.x()-c.left()],temp);
                    }
                }
                else if (delta < 0) // on the top side
                {
                    for (long x = static_cast<long>(std::floor(right_boundary[i-1]))+1; x <= right_x; ++x)
                    {
                        const point p(x, i+top-1);
                        rgb_alpha_pixel temp = alpha_pixel;
                        temp.alpha = static_cast<unsigned char>((right_boundary[i]-x)/std::abs(delta)*max_alpha);
                        if (valid_area.contains(p))
                            assign_pixel(c[p.y()-c.top()][p.x()-c.left()],temp);
                    }
                }
                else // on the bottom side
                {
                    const long old_right_x = static_cast<long>(std::floor(right_boundary[i-1]));
                    for (long x = right_x+1; x <= old_right_x; ++x)
                    {
                        const point p(x, i+top);
                        rgb_alpha_pixel temp = alpha_pixel;
                        temp.alpha = static_cast<unsigned char>((right_boundary[i-1]-x)/delta*max_alpha);
                        if (valid_area.contains(p))
                            assign_pixel(c[p.y()-c.top()][p.x()-c.left()],temp);
                    }
                }
            }
        }
        inline void draw_solid_convex_polygon (
            const canvas& c,
            const std::vector<point>& polygon
        ) { draw_solid_convex_polygon(c, polygon, 0); }

    // ----------------------------------------------------------------------------------------

        template <
            typename image_type
            >
        void draw_image (
            const canvas& c,
            const point& p,
            const image_type& img,
            const rectangle& area_ = rectangle(std::numeric_limits<long>::min(), std::numeric_limits<long>::min(),
                                              std::numeric_limits<long>::max(), std::numeric_limits<long>::max())
        )
        {
            const long x = p.x();
            const long y = p.y();
            rectangle rect(x,y,num_columns(img)+x-1,num_rows(img)+y-1);
            rectangle area = c.intersect(rect).intersect(area_);
            if (area.is_empty())
                return;

            for (long row = area.top(); row <= area.bottom(); ++row)
            {
                for (long col = area.left(); col <= area.right(); ++col)
                {
                    assign_pixel(c[row-c.top()][col-c.left()], img[row-rect.top()][col-rect.left()]);
                }
            }
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename image_type
            >
        void draw_image (
            const canvas& c,
            const rectangle& rect,
            const image_type& img,
            const rectangle& area_ = rectangle(std::numeric_limits<long>::min(), std::numeric_limits<long>::min(),
                                              std::numeric_limits<long>::max(), std::numeric_limits<long>::max())
        )
        {
            const rectangle area = c.intersect(rect).intersect(area_);
            if (area.is_empty() || num_columns(img) * num_rows(img) == 0)
                return;

            const matrix<long,1> x = matrix_cast<long>(round(linspace(0, num_columns(img)-1, rect.width())));
            const matrix<long,1> y = matrix_cast<long>(round(linspace(0, num_rows(img)-1, rect.height())));

            for (long row = area.top(); row <= area.bottom(); ++row)
            {
                const long r = y(row-rect.top());
                long cc = area.left() - rect.left();
                for (long col = area.left(); col <= area.right(); ++col)
                {
                    assign_pixel(c[row-c.top()][col-c.left()], img[r][x(cc++)]);
                }
            }
        }

    // ----------------------------------------------------------------------------------------

        template <typename pixel_type>
        void draw_rounded_rectangle (
            const canvas& c,
            const rectangle& rect,
            unsigned radius,
            const pixel_type& color,
            const rectangle& area_ = rectangle(std::numeric_limits<long>::min(), std::numeric_limits<long>::min(),
                                              std::numeric_limits<long>::max(), std::numeric_limits<long>::max())
        )
        {
            if ( rect.intersect ( c ).is_empty() )
                return;

            draw_line ( c, point(rect.left() + radius + 1, rect.bottom()),
                        point(rect.right() - radius - 1, rect.bottom()), color,area_ );

            draw_line ( c, point(rect.left() + radius + 1, rect.top()),
                        point(rect.right() - radius - 1, rect.top()), color,area_ );

            draw_line ( c, point(rect.left(), rect.top() + radius + 1),
                        point(rect.left(), rect.bottom() - radius - 1), color,area_ );

            draw_line ( c, point(rect.right(), rect.top() + radius + 1),
                        point(rect.right(), rect.bottom() - radius - 1), color,area_ );

            unsigned x = radius, y = 0, old_x = x;

            point p;
            while ( x > y )
            {
                p = point(rect.left() + radius - y, rect.top() + radius - x);
                if (area_.contains(p)) draw_pixel (c, p , color );
                p = point(rect.right() - radius + y, rect.top() + radius - x);
                if (area_.contains(p)) draw_pixel (c, p , color );
                p = point(rect.right() - radius + y, rect.bottom() - radius + x);
                if (area_.contains(p)) draw_pixel (c, p , color );
                p = point(rect.left() + radius - y, rect.bottom() - radius + x);
                if (area_.contains(p)) draw_pixel (c, p , color );
                p = point(rect.left() + radius - x, rect.top() + radius - y);
                if (area_.contains(p)) draw_pixel (c, p , color );
                p = point(rect.right() - radius + x, rect.top() + radius - y);
                if (area_.contains(p)) draw_pixel (c, p , color );
                p = point(rect.right() - radius + x, rect.bottom() - radius + y);
                if (area_.contains(p)) draw_pixel (c, p , color );
                p = point(rect.left() + radius - x, rect.bottom() - radius + y);
                if (area_.contains(p)) draw_pixel (c, p , color );
                y++;
                old_x = x;
                x = square_root ( ( radius * radius - y * y ) * 4 ) / 2;
            }

            if ( x == y && old_x != x )
            {
                p = point(rect.left() + radius - y, rect.top() + radius - x);
                if (area_.contains(p)) draw_pixel (c, p , color );
                p = point(rect.right() - radius + y, rect.top() + radius - x);
                if (area_.contains(p)) draw_pixel (c, p , color );
                p = point(rect.right() - radius + y, rect.bottom() - radius + x);
                if (area_.contains(p)) draw_pixel (c, p , color );
                p = point(rect.left() + radius - y, rect.bottom() - radius + x);
                if (area_.contains(p)) draw_pixel (c, p , color );
            }
        }

    // ----------------------------------------------------------------------------------------

        template <typename pixel_type>
        void fill_gradient_rounded (
            const canvas& c,
            const rectangle& rect,
            unsigned long radius,
            const pixel_type& top_color,
            const pixel_type& bottom_color,
            const rectangle& area = rectangle(std::numeric_limits<long>::min(), std::numeric_limits<long>::min(),
                                              std::numeric_limits<long>::max(), std::numeric_limits<long>::max())

        )
        {
            rectangle valid_area(c.intersect(area.intersect(rect)));
            if ( valid_area.is_empty() )
                return;

            unsigned long m_prev = 0, m = radius, c_div = valid_area.height() - 1;

            const long c_top = valid_area.top();
            const long c_bottom = valid_area.bottom();

            for ( long y = c_top; y <= c_bottom;y++ )
            {

                unsigned long c_s = y - c_top;

                unsigned long c_t = c_bottom - y;

                if ( c_div == 0 )
                {
                    // only a single round, just take the average color
                    c_div = 2;
                    c_s = c_t = 1;
                }

                rgb_alpha_pixel color;
                vector_to_pixel(color,
                                ((pixel_to_vector<unsigned long>(top_color)*c_t + pixel_to_vector<unsigned long>(bottom_color)*c_s)/c_div));

                unsigned long s = y - rect.top();

                unsigned long t = rect.bottom() - y;

                if ( s < radius )
                {
                    m = radius - square_root ( ( radius * radius - ( radius - s ) * ( radius - s ) ) * 4 ) / 2;

                    if ( s == m && m + 1 < m_prev )  // these are hacks to remove distracting artefacts at small radii
                        m++;
                }
                else if ( t < radius )
                {
                    m = radius - square_root ( ( radius * radius - ( radius - t ) * ( radius - t ) ) * 4 ) / 2;

                    if ( t == m && m == m_prev )
                        m++;
                }
                else
                {
                    m = 0;
                }

                m_prev = m;

                draw_line ( c, point(rect.left() + m, y),
                            point(rect.right() - m, y), color, valid_area );
            }
        }

    // ----------------------------------------------------------------------------------------

        template <typename pixel_type>
        void draw_rectangle (
            const canvas& c,
            rectangle rect,
            const pixel_type& pixel,
            const rectangle& area = rectangle(std::numeric_limits<long>::min(), std::numeric_limits<long>::min(),
                                              std::numeric_limits<long>::max(), std::numeric_limits<long>::max())
        )
        {
            // top line
            draw_line(c, point(rect.left(),rect.top()),
                      point(rect.right(),rect.top()),
                      pixel, area);

            // bottom line
            draw_line(c, point(rect.left(),rect.bottom()),
                      point(rect.right(),rect.bottom()),
                      pixel, area);

            // left line
            draw_line(c, point(rect.left(),rect.top()),
                      point(rect.left(),rect.bottom()),
                      pixel, area);

            // right line
            draw_line(c, point(rect.right(),rect.top()),
                      point(rect.right(),rect.bottom()),
                      pixel, area);
        }
        inline void draw_rectangle (
            const canvas& c,
            rectangle rect
        ){ draw_rectangle(c, rect, 0); }

    // ----------------------------------------------------------------------------------------

        template <typename pixel_type>
        void fill_rect (
            const canvas& c,
            const rectangle& rect,
            const pixel_type& pixel
        )
        {
            rectangle area = rect.intersect(c);
            for (long y = area.top(); y <= area.bottom(); ++y)
            {
                for (long x = area.left(); x <= area.right(); ++x)
                {
                    assign_pixel(c[y-c.top()][x-c.left()], pixel);
                }
            }
        }

    // ----------------------------------------------------------------------------------------

        template <typename pixel_type>
        void fill_rect_with_vertical_gradient (
            const canvas& c,
            const rectangle& rect,
            const pixel_type& pixel_top,
            const pixel_type& pixel_bottom,
            const rectangle& area_ = rectangle(std::numeric_limits<long>::min(), std::numeric_limits<long>::min(),
                                              std::numeric_limits<long>::max(), std::numeric_limits<long>::max())
        )
        {
            rectangle area = rect.intersect(c).intersect(area_);
            pixel_type pixel;

            const long s = rect.bottom()-rect.top();

            for (long y = area.top(); y <= area.bottom(); ++y)
            {
                const long t = rect.bottom()-y;
                const long b = y-rect.top();
                vector_to_pixel(pixel,
                        ((pixel_to_vector<long>(pixel_top)*t +
                          pixel_to_vector<long>(pixel_bottom)*b)/s));

                for (long x = area.left(); x <= area.right(); ++x)
                {
                    assign_pixel(c[y-c.top()][x-c.left()], pixel);
                }
            }
        }

    // ----------------------------------------------------------------------------------------

    }

    #ifdef NO_MAKEFILE
    #include "canvas_drawing.cpp"
    #endif

    #endif // DLIB_GUI_CANVAS_DRAWINg_