From 79883302ac4e1b85d2afd9adcad78646757304ac Mon Sep 17 00:00:00 2001
From: "yang.yongquan" <3395816735@qq.com>
Date: Tue, 13 Sep 2022 21:01:18 +0800
Subject: [PATCH] =?UTF-8?q?=E5=A2=9E=E5=8A=A0=E4=BA=86=E5=88=86=E5=89=B2?=
 =?UTF-8?q?=E7=9A=84=E8=B4=9D=E5=A1=9E=E5=B0=94=E6=9B=B2=E7=BA=BF=E7=9A=84?=
 =?UTF-8?q?=E6=8E=A7=E5=88=B6=E7=82=B9?=
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---
 .../ArchitectureColoredPainting.vcxproj       |  2 +
 ...rchitectureColoredPainting.vcxproj.filters |  6 ++
 .../CubicMonotonization.cpp                   | 73 +++++++++++++++++++
 .../CubicMonotonization.h                     | 24 ++++++
 4 files changed, 105 insertions(+)
 create mode 100644 ArchitectureColoredPainting/CubicMonotonization.cpp
 create mode 100644 ArchitectureColoredPainting/CubicMonotonization.h

diff --git a/ArchitectureColoredPainting/ArchitectureColoredPainting.vcxproj b/ArchitectureColoredPainting/ArchitectureColoredPainting.vcxproj
index 62c0450..dc95cf0 100644
--- a/ArchitectureColoredPainting/ArchitectureColoredPainting.vcxproj
+++ b/ArchitectureColoredPainting/ArchitectureColoredPainting.vcxproj
@@ -87,6 +87,7 @@
   <ItemGroup>
     <ClCompile Include="BvhTree.cpp" />
     <ClCompile Include="Camera.cpp" />
+    <ClCompile Include="CubicMonotonization.cpp" />
     <ClCompile Include="Light.cpp" />
     <ClCompile Include="Mesh.cpp" />
     <ClCompile Include="Model.cpp" />
@@ -123,6 +124,7 @@
   <ItemGroup>
     <ClInclude Include="BvhTree.h" />
     <ClInclude Include="Camera.h" />
+    <ClInclude Include="CubicMonotonization.h" />
     <ClInclude Include="Drawable.h" />
     <ClInclude Include="Light.h" />
     <ClInclude Include="Mesh.h" />
diff --git a/ArchitectureColoredPainting/ArchitectureColoredPainting.vcxproj.filters b/ArchitectureColoredPainting/ArchitectureColoredPainting.vcxproj.filters
index ed08f43..092c1d5 100644
--- a/ArchitectureColoredPainting/ArchitectureColoredPainting.vcxproj.filters
+++ b/ArchitectureColoredPainting/ArchitectureColoredPainting.vcxproj.filters
@@ -67,6 +67,9 @@
     <ClCompile Include="Light.cpp">
       <Filter>Source Files</Filter>
     </ClCompile>
+    <ClCompile Include="CubicMonotonization.cpp">
+      <Filter>Source Files</Filter>
+    </ClCompile>
   </ItemGroup>
   <ItemGroup>
     <QtMoc Include="RendererWidget.h">
@@ -148,5 +151,8 @@
     <ClInclude Include="Light.h">
       <Filter>Header Files</Filter>
     </ClInclude>
+    <ClInclude Include="CubicMonotonization.h">
+      <Filter>Header Files</Filter>
+    </ClInclude>
   </ItemGroup>
 </Project>
\ No newline at end of file
diff --git a/ArchitectureColoredPainting/CubicMonotonization.cpp b/ArchitectureColoredPainting/CubicMonotonization.cpp
new file mode 100644
index 0000000..8e96f1b
--- /dev/null
+++ b/ArchitectureColoredPainting/CubicMonotonization.cpp
@@ -0,0 +1,73 @@
+#include "CubicMonotonization.h"
+
+const double CubicMonotonization::eps = 1e-6;
+
+
+CubicMonotonization::point CubicMonotonization::getPointByT(point a, point b, double t) const {
+	return { a.first * (1 - t) + b.first, a.second * (1 - t) + b.second };
+}
+
+
+void CubicMonotonization::findPointsOfDivison(vector<double> p, vector<double>& res) {
+	double a = -p[0] + 7 * p[1] - 9 * p[2] + 3 * p[3];
+	double b = 6 * p[0] - 12 * p[1] + 6 * p[2];
+	double c = -3 * p[0] + 3*p[1];
+	double deta = b * b - 4*a*c;
+	if (fabs(deta) < eps) return;
+	double t = 0;
+	if (fabs(a) <= eps) {
+		deta = sqrt(deta);
+		t = -b + deta;
+		if (0 < t && t < 1) {
+			res.push_back(t);
+		}
+		if (fabs(deta) <= eps) return ;
+		t = -b - deta;
+		if (0 < t && t < 1) {
+			res.push_back(t);
+		}
+	}
+}
+
+double CubicMonotonization::getBezierPoint(vector<double> &p, double t) const{
+	double pt = 1 - t;
+	return pt * pt * pt * p[0] + 3 * t * pt * pt * p[1] + 3 * t * t * pt * p[2] + t * t * t * p[3];
+}
+
+void CubicMonotonization::splitBezierCubic(Line& p, point mid, double t, vector <Line>& res) {
+	Line Lf; Lf.clear();
+	double pt = 1 - t;
+	Lf.push_back(p[0]);
+	point pointF = getPointByT(p[0], p[1], t);
+	point pointG = getPointByT(p[1], p[2], t);
+	point pointH = getPointByT(p[2], p[3], t);
+	Lf.push_back(pointF);
+	Lf.push_back(getPointByT(pointF, pointG, t));
+	Lf.push_back(mid);
+	res.push_back(Lf);
+	p[0] = mid;
+	p[1] = getPointByT(pointG, pointH, t);
+	p[2] = pointH;
+}
+
+void CubicMonotonization::getPointsOfDivision(Line p, vector <Line>& res) {
+	vector<double> vX, vY, re;
+	vX.clear();
+	vY.clear();
+	re.clear();
+	for (point now : p) {
+		vX.push_back(now.first);
+		vY.push_back(now.second);
+	}
+	findPointsOfDivison(vX, re);
+	findPointsOfDivison(vY, re);
+	sort(re.begin(), re.end());
+	double lt = 0, x = 0, y = 0;
+	for (double &t : re) {
+		if (fabs(t - lt) <= eps) continue;
+		x = getBezierPoint(vX, t);
+		y = getBezierPoint(vY, t);
+		splitBezierCubic(p, { x, y }, t, res);
+		lt = t;
+	}
+}
diff --git a/ArchitectureColoredPainting/CubicMonotonization.h b/ArchitectureColoredPainting/CubicMonotonization.h
new file mode 100644
index 0000000..6531b27
--- /dev/null
+++ b/ArchitectureColoredPainting/CubicMonotonization.h
@@ -0,0 +1,24 @@
+#include <utility>
+#include <vector>
+#include <algorithm>
+#pragma once
+using std::pair;
+using std::vector;
+using std::min;
+using std::max;
+using std::sort;
+class CubicMonotonization
+{
+typedef pair<double, double> point;
+typedef vector<point> Line;
+private:
+	static const double eps;
+	point getPointByT(point a, point b, double t) const;
+	void findPointsOfDivison(vector<double> p, vector<double> &res);
+	double getBezierPoint(vector<double> &p, double t) const;
+	void splitBezierCubic(Line& p, point mid, double t, vector <Line> &res);
+public:
+	// p 为端点、控制点、控制点、端点， res 为所有导数为0的点
+	void getPointsOfDivision(Line p, vector <Line> &res);
+};
+