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Classify Beziers, use DeCasteljau for CPU renderer
authorSam Moore <[email protected]>
Mon, 1 Sep 2014 12:55:55 +0000 (20:55 +0800)
committerSam Moore <[email protected]>
Mon, 1 Sep 2014 12:55:55 +0000 (20:55 +0800)
I don't know how glDrawLines does it, but I can't get rid of the wiggles in straight lines done using CPU renderer.
So I switched to DeCasteljau.

Then I made it classify the lines and only use one Bresenham instead of 100 anyway.

src/bezier.cpp patch | blob | history
src/bezier.h patch | blob | history
src/objectrenderer.cpp patch | blob | history
src/rational.h patch | blob | history
src/real.h patch | blob | history
src/svg-tests/fox_simple.svg [new file with mode: 0644] patch | blob
src/svg-tests/kinematic_diagram.svg [new file with mode: 0644] patch | blob
src/svg-tests/lines.svg patch | blob | history

diff --git a/src/bezier.cpp b/src/bezier.cpp
index 3fa16e3..9d24672 100644 (file)
--- a/src/bezier.cpp
+++ b/src/bezier.cpp
@@ -166,8 +166,8 @@ pair<Real, Real> BezierTurningPoints(const Real & p0, const Real & p1, const Rea
        {
                return pair<Real,Real>(0, 1);
        }
-       Real a = (3*(p1-p2) + p3 - p0);
-       Real b = 2*(p2 - 2*p1 + p0);
+       Real a = ((p1-p2)*3 + p3 - p0);
+       Real b = (p2 - p1*2 + p0)*2;
        Real c = (p1-p0);
        if (a == 0)
        {
@@ -179,7 +179,7 @@ pair<Real, Real> BezierTurningPoints(const Real & p0, const Real & p1, const Rea
                return pair<Real, Real>(t, t);
        }
        //Debug("a, b, c are %f, %f, %f", Float(a), Float(b), Float(c));
-       if (b*b - 4*a*c < 0)
+       if (b*b - a*c*4 < 0)
        {
                //Debug("No real roots");
                return pair<Real, Real>(0,1);
diff --git a/src/bezier.h b/src/bezier.h
index 7ff4f87..a7124af 100644 (file)
--- a/src/bezier.h
+++ b/src/bezier.h
@@ -25,16 +25,72 @@ namespace IPDF
                Real x2; Real y2;
                Real x3; Real y3;
                
-               typedef enum {LINE, QUADRATIC, CUSP, LOOP, SERPENTINE} Type;
+               typedef enum {UNKNOWN, LINE, QUADRATIC, CUSP, LOOP, SERPENTINE} Type;
                Type type;
                
                Bezier() = default; // Needed so we can fread/fwrite this struct... for now.
-               Bezier(Real _x0, Real _y0, Real _x1, Real _y1, Real _x2, Real _y2, Real _x3, Real _y3) : x0(_x0), y0(_y0), x1(_x1), y1(_y1), x2(_x2), y2(_y2), x3(_x3), y3(_y3) 
+               Bezier(Real _x0, Real _y0, Real _x1, Real _y1, Real _x2, Real _y2, Real _x3, Real _y3) : x0(_x0), y0(_y0), x1(_x1), y1(_y1), x2(_x2), y2(_y2), x3(_x3), y3(_y3), type(UNKNOWN)
                {
-                       //TODO: classify the curve
-                       type = SERPENTINE;
+
                }
                
+               const Type & GetType()
+               {
+                       if (type != Bezier::UNKNOWN)
+                               return type;
+                       // From Loop-Blinn 2005, with w0 == w1 == w2 == w3 = 1
+                       // Transformed control points: (a0 = x0, b0 = y0)
+                       Real a1 = (x1-x0)*3;
+                       Real a2 = (x0- x1*2 +x2)*3;
+                       Real a3 = (x3 - x0 + (x1 - x2)*3);
+                       
+                       Real b1 = (y1-y0)*3;
+                       Real b2 = (y0- y1*2 +y2)*3;
+                       Real b3 = (y3 - y0 + (y1 - y2)*3);
+                       
+                       // d vector (d0 = 0 since all w = 1)
+                       Real d1 = a2*b3 - a3*b2;
+                       Real d2 = a3*b1 - a1*b3;
+                       Real d3 = a1*b2 - a2*b1;
+                       
+                       if (d1 == d2 && d2 == d3 && d3 == 0)
+                       {
+                               type = LINE;
+                               //Debug("LINE %s", Str().c_str());
+                               return type;
+                       }
+                       
+                       Real delta1 = -d1*d1;
+                       Real delta2 = d1*d2;
+                       Real delta3 = d1*d3 -d2*d2;
+                       if (delta1 == delta2 && delta2 == delta3 && delta3 == 0)
+                       {
+                               type = QUADRATIC;
+                               
+                               //Debug("QUADRATIC %s", Str().c_str());
+                               return type;
+                       }
+                       
+                       Real discriminant = d1*d3*4 -d2*d2;
+                       if (discriminant == 0)
+                       {
+                               type = CUSP;
+                               //Debug("CUSP %s", Str().c_str());
+                       }
+                       else if (discriminant > 0)
+                       {
+                               type = SERPENTINE;
+                               //Debug("SERPENTINE %s", Str().c_str());
+                       }
+                       else
+                       {
+                               type = LOOP;
+                               //Debug("LOOP %s", Str().c_str());
+                       }
+                       return type;
+               }
+               
+               
                std::string Str() const
                {
                        std::stringstream s;
@@ -46,7 +102,7 @@ namespace IPDF
                 * Construct absolute control points using relative control points to a bounding rectangle
                 * ie: If cpy is relative to bounds rectangle, this will be absolute
                 */
-               Bezier(const Bezier & cpy, const Rect & t = Rect(0,0,1,1)) : x0(cpy.x0), y0(cpy.y0), x1(cpy.x1), y1(cpy.y1), x2(cpy.x2),y2(cpy.y2), x3(cpy.x3), y3(cpy.y3), type(cpy.type)
+               Bezier(const Bezier & cpy, const Rect & t = Rect(0,0,1,1)) : x0(cpy.x0), y0(cpy.y0), x1(cpy.x1), y1(cpy.y1), x2(cpy.x2),y2(cpy.y2), x3(cpy.x3), y3(cpy.y3), type(UNKNOWN)
                {
                        x0 *= t.w;
                        y0 *= t.h;
diff --git a/src/objectrenderer.cpp b/src/objectrenderer.cpp
index f39bae8..4e59cd0 100644 (file)
--- a/src/objectrenderer.cpp
+++ b/src/objectrenderer.cpp
@@ -7,6 +7,7 @@
 #include "view.h"
 #include <vector>
 #include <queue>
+#include <stack>
 
 using namespace std;
 
@@ -254,36 +255,50 @@ void BezierRenderer::RenderUsingCPU(const Objects & objects, const View & view,
                                                                                
 
                
-               Real x[2]; Real y[2];
-               control.Evaluate(x[0], y[0], Real(0));
-               //Debug("target is (%lu, %lu)", target.w, target.h);
-               int64_t blen = min(max((int64_t)2, (int64_t)(target.w/view.GetBounds().w)), (int64_t)100);
+       
+               unsigned blen = min(max(2U, (unsigned)(target.w/view.GetBounds().w)), min((unsigned)(pix_bounds.w+pix_bounds.h)/4 + 1, 100U));
                
-               Real invblen(1); invblen /= blen;
-               //Debug("Using %li lines, inverse %f", blen, Double(invblen));
-               for (int64_t j = 1; j <= blen; ++j)
+               // DeCasteljau Divide the Bezier
+               queue<Bezier> divisions;
+               divisions.push(control);
+               while(divisions.size() < blen)
                {
-                       control.Evaluate(x[j % 2],y[j % 2], invblen*j);
-                       ObjectRenderer::RenderLineOnCPU((int64_t)Double(x[0]),(int64_t)Double(y[0]), (int64_t)Double(x[1]),(int64_t)Double(y[1]), target, Colour(0,0,0,!view.PerformingShading()));
+                       Bezier & current = divisions.front();
+                       if (current.GetType() == Bezier::LINE)
+                       {
+                               --blen;
+                               continue;
+                       }
+                       divisions.push(current.DeCasteljauSubdivideRight(Real(1)/Real(2)));     
+                       divisions.push(current.DeCasteljauSubdivideLeft(Real(1)/Real(2)));
+                       divisions.pop();
+                       
+                       //Debug("divisions %u", divisions.size());
+               }
+               while (divisions.size() > 0)
+               {
+                       Bezier & current = divisions.front();
+                       RenderLineOnCPU(current.x0, current.y0, current.x3, current.y3, target, Colour(0,0,0,!view.PerformingShading()));
+                       divisions.pop();
                }
                
-               /*
-               Real u(0);
-               while (u < Real(1))
+               /* Draw the Bezier by sampling
+               Real invblen(1); invblen /= blen;
+               Real t(invblen);
+               Vec2 v0;
+               Vec2 v1;
+               control.Evaluate(v0.x, v0.y, 0);
+               for (int64_t j = 1; j <= blen; ++j)
                {
-                       u += Real(1e-6);
-                       Real x; Real y; control.Evaluate(x,y,u);
-                       int64_t index = ((int64_t)x + (int64_t)y*target.w)*4;
-                       if (index >= 0 && index < 4*(target.w*target.h))
-                       {
-                               target.pixels[index+0] = 0;
-                               target.pixels[index+1] = 0;
-                               target.pixels[index+2] = 0;
-                               target.pixels[index+3] = 255;
-                       }       
+                       control.Evaluate(v1.x, v1.y, t);
+                       
+                       ObjectRenderer::RenderLineOnCPU(v0.x, v0.y, v1.x, v1.y, target, Colour(0,0,0,!view.PerformingShading()));
+                       //ObjectRenderer::SetColour(target, x[0], y[0], Colour(1,0,0,1));
+                       //ObjectRenderer::SetColour(target, x[1], y[1], Colour(0,0,1,1));
+                       t += invblen;
+                       v0 = v1;
                }
                */
-               
        }
 }
 
diff --git a/src/rational.h b/src/rational.h
index b019505..f9157c7 100644 (file)
--- a/src/rational.h
+++ b/src/rational.h
@@ -77,6 +77,8 @@ struct Rational
        {
                Simplify();
        }
+       
+
 
        Rational(const T & _P, const T & _Q) : P(_P), Q(_Q)
        {
@@ -174,7 +176,7 @@ struct Rational
        double ToDouble() const 
        {
                T num = P, denom = Q;
-               while (Tabs(num) > T(DBL_MAX))
+               while (Tabs(num) > T(1e10))
                {
                        num /= T(16);
                        denom /= T(16);
@@ -206,8 +208,6 @@ struct Rational
 
 
 
-
-
 }
 
 #endif //_RATIONAL_H
diff --git a/src/real.h b/src/real.h
index b766558..322b02b 100644 (file)
--- a/src/real.h
+++ b/src/real.h
@@ -81,7 +81,6 @@ namespace IPDF
                        r *= a;
                return r;
        }
-       
        struct Vec2
        {
                Real x;
@@ -89,6 +88,7 @@ namespace IPDF
                Vec2() : x(0), y(0) {}
                Vec2(Real _x, Real _y) : x(_x), y(_y) {}
                Vec2(const std::pair<Real, Real> & p) : x(p.first), y(p.second) {}
+               Vec2(const std::pair<int64_t, int64_t> & p) : x(p.first), y(p.second) {}
        
                bool operator==(const Vec2& other) const { return (x == other.x) && (y == other.y); }
                bool operator!=(const Vec2& other) const { return !(*this == other); }
diff --git a/src/svg-tests/fox_simple.svg b/src/svg-tests/fox_simple.svg
new file mode 100644 (file)
index 0000000..58e2b8a
--- /dev/null
+++ b/src/svg-tests/fox_simple.svg
@@ -0,0 +1,235 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   xmlns:dc="http://purl.org/dc/elements/1.1/"
+   xmlns:cc="http://creativecommons.org/ns#"
+   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
+   xmlns:svg="http://www.w3.org/2000/svg"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   width="339.96875"
+   height="174.53125"
+   id="svg3022"
+   version="1.1"
+   inkscape:version="0.48.4 r9939"
+   sodipodi:docname="fox_simple.svg"
+   inkscape:export-filename="/home/sam/Documents/University/2014/ipdf/sam/figures/fox2.png"
+   inkscape:export-xdpi="90"
+   inkscape:export-ydpi="90">
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+     id="defs3024" />
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+         rdf:about="">
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diff --git a/src/svg-tests/kinematic_diagram.svg b/src/svg-tests/kinematic_diagram.svg
new file mode 100644 (file)
index 0000000..ca35cc2
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+       id="text4797-8-8-7-2-6"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan4799-3-4-96-8-0"
+         x="536.61084"
+         y="397.08331"
+         style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:DejaVu Serif;-inkscape-font-specification:DejaVu Serif Italic">3</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:11.60449505px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:center;line-height:125%;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;font-family:ComicSans;-inkscape-font-specification:ComicSans"
+       x="79.227173"
+       y="385.02295"
+       id="text5114"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan5116"
+         x="79.227173"
+         y="385.02295"
+         style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-family:DejaVu Sans;-inkscape-font-specification:DejaVu Sans">Original NUWAR Arm</tspan><tspan
+         sodipodi:role="line"
+         x="79.227173"
+         y="399.52856"
+         style="font-style:oblique;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:DejaVu Sans;-inkscape-font-specification:DejaVu Sans Oblique"
+         id="tspan5120">n = 17, f = 21, f = 0, f = 0</tspan><tspan
+         sodipodi:role="line"
+         x="79.227173"
+         y="414.03418"
+         style="font-style:oblique;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:DejaVu Sans;-inkscape-font-specification:DejaVu Sans Oblique"
+         id="tspan5222">Mobility = -4</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:11.60449505px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:center;line-height:125%;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;font-family:ComicSans;-inkscape-font-specification:ComicSans"
+       x="289.65292"
+       y="382.59662"
+       id="text5114-9"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan5116-2"
+         x="289.65292"
+         y="382.59662"
+         style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-family:DejaVu Sans;-inkscape-font-specification:DejaVu Sans">Variation #1</tspan><tspan
+         sodipodi:role="line"
+         x="289.65292"
+         y="397.10223"
+         style="font-style:oblique;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:DejaVu Sans;-inkscape-font-specification:DejaVu Sans Oblique"
+         id="tspan5120-5">n = 11, f = 3, f = 0, f = 12</tspan><tspan
+         sodipodi:role="line"
+         x="291.50012"
+         y="411.60785"
+         style="font-style:oblique;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:DejaVu Sans;-inkscape-font-specification:DejaVu Sans Oblique"
+         id="tspan5224">Mobility = 9 </tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:11.60449505px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:center;line-height:125%;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;font-family:ComicSans;-inkscape-font-specification:ComicSans"
+       x="487.25211"
+       y="380.3909"
+       id="text5114-9-2"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan5116-2-4"
+         x="487.25211"
+         y="380.3909"
+         style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-family:DejaVu Sans;-inkscape-font-specification:DejaVu Sans">Variation #2</tspan><tspan
+         sodipodi:role="line"
+         x="487.25211"
+         y="394.89651"
+         style="font-style:oblique;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:DejaVu Sans;-inkscape-font-specification:DejaVu Sans Oblique"
+         id="tspan5120-5-4">n = 11, f = 3, f = 6, f = 6</tspan><tspan
+         sodipodi:role="line"
+         x="487.25211"
+         y="409.40213"
+         style="font-style:oblique;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:DejaVu Sans;-inkscape-font-specification:DejaVu Sans Oblique"
+         id="tspan5226">Mobility = 3</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:11.43720245px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:start;line-height:125%;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;font-family:DejaVu Serif;-inkscape-font-specification:DejaVu Serif"
+       x="547.46826"
+       y="200.76332"
+       id="text5214"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan5216"
+         x="547.46826"
+         y="200.76332">* The base and travelling plate </tspan><tspan
+         sodipodi:role="line"
+         x="547.46826"
+         y="215.05983"
+         id="tspan5220">   are common to all 3 arms</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:4.49763489px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:center;line-height:125%;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;font-family:ComicSans;-inkscape-font-specification:ComicSans"
+       x="264.1481"
+       y="398.80005"
+       id="text4797-8-8-7-3"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan4799-3-4-96-1"
+         x="264.1481"
+         y="398.80005"
+         style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:DejaVu Serif;-inkscape-font-specification:DejaVu Serif Italic">1</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:4.49763489px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:center;line-height:125%;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;font-family:ComicSans;-inkscape-font-specification:ComicSans"
+       x="300.40652"
+       y="398.53168"
+       id="text4797-8-8-7-2-1"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan4799-3-4-96-8-2"
+         x="300.40652"
+         y="398.53168"
+         style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:DejaVu Serif;-inkscape-font-specification:DejaVu Serif Italic">2</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:4.49763489px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:center;line-height:125%;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;font-family:ComicSans;-inkscape-font-specification:ComicSans"
+       x="335.83548"
+       y="399.09357"
+       id="text4797-8-8-7-2-6-4"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan4799-3-4-96-8-0-2"
+         x="335.83548"
+         y="399.09357"
+         style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:DejaVu Serif;-inkscape-font-specification:DejaVu Serif Italic">3</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:4.49763489px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:center;line-height:125%;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;font-family:ComicSans;-inkscape-font-specification:ComicSans"
+       x="54.012356"
+       y="399.62418"
+       id="text4797-8-8-7-1"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan4799-3-4-96-9"
+         x="54.012356"
+         y="399.62418"
+         style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:DejaVu Serif;-inkscape-font-specification:DejaVu Serif Italic">1</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:4.49763489px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:center;line-height:125%;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;font-family:ComicSans;-inkscape-font-specification:ComicSans"
+       x="96.581543"
+       y="399.57596"
+       id="text4797-8-8-7-2-8"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan4799-3-4-96-8-1"
+         x="96.581543"
+         y="399.57596"
+         style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:DejaVu Serif;-inkscape-font-specification:DejaVu Serif Italic">2</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:4.49763489px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:center;line-height:125%;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;font-family:ComicSans;-inkscape-font-specification:ComicSans"
+       x="132.01048"
+       y="400.13782"
+       id="text4797-8-8-7-2-6-8"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan4799-3-4-96-8-0-7"
+         x="132.01048"
+         y="400.13782"
+         style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:DejaVu Serif;-inkscape-font-specification:DejaVu Serif Italic">3</tspan></text>
+  </g>
+</svg>
diff --git a/src/svg-tests/lines.svg b/src/svg-tests/lines.svg
index f15c961..ff7eddb 100644 (file)
--- a/src/svg-tests/lines.svg
+++ b/src/svg-tests/lines.svg
@@ -5,17 +5,20 @@
 <svg xmlns="http://www.w3.org/2000/svg"
      xmlns:xlink="http://www.w3.org/1999/xlink"
      width="400" height="400">
-    <line x1="0" y1="0" x2="400" y2="0" stroke="red"/>
+    <!--<line x1="0" y1="0" x2="400" y2="0" stroke="red"/>-->
     
-    <line x1="0" y1="0" x2="0" y2="400" stroke="red"/>
+    <!--<line x1="0" y1="0" x2="0" y2="400" stroke="red"/>-->
     
-    <line x1="400" y1="0" x2="400" y2="400" stroke="red"/>
+    <!--<line x1="400" y1="0" x2="400" y2="400" stroke="red"/>-->
     
-    <line x1="0" y1="400" x2="400" y2="400" stroke="red"/>
+    <!--<line x1="0" y1="400" x2="400" y2="400" stroke="red"/>-->
     
-       <line 
+       <!--<line
                x1="0" y1="0" x2="400" y2="400" stroke="black"/>
-
+       -->
        <line
-               x1="400" y1="0" x2="0" y2="400" stroke="black"/>
+               x1="0" y1="200" x2="400" y2="0" stroke="black"/>
+               
+       <!--<line
+               x1="200" y1="200" x2="400" y2="100" stroke="black"/>-->
 </svg>
Infinite Precision Document Formats - Code base

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