diff --git a/GeoLib/Point.cpp b/GeoLib/Point.cpp
index abdd9590de73bb0a0761eaaf4c708d2482a700ba..92efe2c8c87ff51313e03dc3599c480e6783039f 100644
--- a/GeoLib/Point.cpp
+++ b/GeoLib/Point.cpp
@@ -12,48 +12,66 @@
#include <cmath>
-#include <limits>
#include "Point.h"
namespace GeoLib {
-bool lessX (GeoLib::Point const & p0, GeoLib::Point const & p1)
+bool operator<= (const GeoLib::Point& p0, const GeoLib::Point& p1)
{
- if (p0[0] <= p1[0]) return true;
- return false;
-}
+ if (p0[0] > p1[0]) {
+ return false;
+ } else {
+ if (p0[0] < p1[0]) {
+ return true;
+ }
+ }
+ // => p0[0] == p1[0]
-bool lessY (GeoLib::Point const & p0, GeoLib::Point const & p1)
-{
- if (p0[1] <= p1[1]) return true;
- return false;
-}
+ if (p0[1] > p1[1]) {
+ return false;
+ } else {
+ if (p0[1] < p1[1]) {
+ return true;
+ }
+ }
+ // => p0[1] == p1[1]
-bool lessZ (GeoLib::Point const & p0, GeoLib::Point const & p1)
-{
- if (p0[2] <= p1[2]) return true;
- return false;
+ if (p0[2] > p1[2]) {
+ return false;
+ } else {
+ return true;
+ }
}
-bool operator<= (const GeoLib::Point& p0, const GeoLib::Point& p1)
+bool lessEq(const GeoLib::Point& p0, const GeoLib::Point& p1, double tol)
{
- double tol (sqrt (std::numeric_limits<double>::min()));
-
- if (fabs (p0[0]-p1[0]) > tol * fabs(p0[0])) {
- if (p0[0] < p1[0]) return true;
- else return false;
+ // test a relative and an absolute criterion
+ if (fabs(p0[0]-p1[0]) > tol * std::min(fabs(p1[0]), fabs(p0[0])) && fabs(p0[0]-p1[0]) > tol) {
+ if (p0[0] <= p1[0])
+ return true;
+ else
+ return false;
} else {
// assume p0[0] == p1[0]
- if (fabs (p0[1]-p1[1]) > tol * fabs(p0[1])) {
- if (p0[1] < p1[1]) return true;
- else return false;
+ if (fabs (p0[1]-p1[1]) > tol * fabs(p0[1]) && fabs(p0[1]-p1[1]) > tol) {
+ if (p0[1] <= p1[1])
+ return true;
+ else
+ return false;
} else {
// assume p0[1] == p1[1] and p0[0] == p1[0]
- if (p0[2] < p1[2]) return true;
- else return false;
+ if (fabs (p0[2]-p1[2]) > tol * fabs(p0[2]) && fabs(p0[2]-p1[2]) > tol) {
+ if (p0[2] <= p1[2])
+ return true;
+ else
+ return false;
+ } else {
+ return true;
+ }
}
}
}
+
} // end namespace GeoLib
diff --git a/GeoLib/Point.h b/GeoLib/Point.h
index e793ef5b3e7fc818cf679838c210f9ee628d96a4..cd4c0728344085eff867eedf73fc5f9dc57bcf0a 100644
--- a/GeoLib/Point.h
+++ b/GeoLib/Point.h
@@ -13,6 +13,8 @@
#ifndef POINT_H_
#define POINT_H_
+#include <limits>
+
#include "TemplatePoint.h"
namespace GeoLib {
@@ -24,33 +26,19 @@ namespace GeoLib {
typedef TemplatePoint<double> Point;
/**
- * comparison based on the x coordinate
- * @param p0 first point
- * @param p1 second point
- * @return true if the x coordinate of p0 is smaller equal the x coordinate of p1, else false
- */
-bool lessX (Point const & p0, Point const & p1);
-
-/**
- * comparison based on the y coordinate
- * @param p0 first point
- * @param p1 second point
- * @return true if the y coordinate of p0 is smaller equal the y coordinate of p1, else false
- */
-bool lessY (Point const & p0, Point const & p1);
-
-/**
- * comparison based on the z coordinate
- * @param p0 first point
- * @param p1 second point
- * @return true if the z coordinate of p0 is smaller equal the z coordinate of p1, else false
+ * lexicographic comparison of points
*/
-bool lessZ (Point const & p0, Point const & p1);
+bool operator<= (GeoLib::Point const & p0, GeoLib::Point const & p1);
/**
- * lexicographic comparison of points
+ * lexicographical comparison of points taking an epsilon into account
+ * @param p0 first input Point
+ * @param p1 first input Point
+ * @param tol tolerance (if in the comparison operation the property fabs(p0[k] - p1[k]) < tol
+ * holds for the k-th coordinate the points are assumed the be equal in this coordinate)
+ * @return true, if p0 is lexicographically smaller than p1
*/
-bool operator<= (GeoLib::Point const & p0, GeoLib::Point const & p1);
+bool lessEq(const GeoLib::Point& p0, const GeoLib::Point& p1, double tol = std::numeric_limits<double>::epsilon());
}
diff --git a/Tests/GeoLib/TestPoint.cpp b/Tests/GeoLib/TestPoint.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..ef0c08f3fca15462151f483f716adc7a687fa73a
--- /dev/null
+++ b/Tests/GeoLib/TestPoint.cpp
@@ -0,0 +1,157 @@
+/**
+ * @file TestPoint.cpp
+ * @author Thomas Fischer
+ * @date Nov 8, 2012
+ *
+ * @copyright
+ * Copyright (c) 2012, OpenGeoSys Community (http://www.opengeosys.org)
+ * Distributed under a Modified BSD License.
+ * See accompanying file LICENSE.txt or
+ * http://www.opengeosys.org/LICENSE.txt
+ */
+
+#include <ctime>
+#include "gtest/gtest.h"
+
+#include "Point.h"
+
+using namespace GeoLib;
+
+TEST(GeoLib, PointComparisonLessEq)
+{
+ // first coordinate
+ ASSERT_TRUE(lessEq(Point(0,1,1),Point(1,1,1)));
+ ASSERT_FALSE(lessEq(Point(1,1,1),Point(0,1,1)));
+ // second coordinate
+ ASSERT_TRUE(lessEq(Point(1,0,1),Point(1,1,1)));
+ ASSERT_FALSE(lessEq(Point(1,1,1),Point(1,0,1)));
+ // third coordinate
+ ASSERT_TRUE(lessEq(Point(1,1,0),Point(1,1,1)));
+ ASSERT_FALSE(lessEq(Point(1,1,1),Point(1,1,0)));
+
+ const double e(2*std::numeric_limits<double>::epsilon());
+ // first coordinate
+ ASSERT_TRUE(lessEq(Point(1-e,1,1),Point(1,1,1)));
+ ASSERT_FALSE(lessEq(Point(1,1,1),Point(1-e,1,1)));
+ // second coordinate
+ ASSERT_TRUE(lessEq(Point(1,1-e,1),Point(1,1,1)));
+ ASSERT_FALSE(lessEq(Point(1,1,1),Point(1,1-e,1)));
+ // third coordinate
+ ASSERT_TRUE(lessEq(Point(1,1,1-e),Point(1,1,1)));
+ ASSERT_FALSE(lessEq(Point(1,1,1),Point(1,1,1-e)));
+
+ ASSERT_TRUE(lessEq(Point(1,1,1),Point(1,1,1)));
+
+ const double half_eps(0.5*std::numeric_limits<double>::epsilon());
+ ASSERT_TRUE(lessEq(Point(1+half_eps,1,1),Point(1,1,1)));
+ ASSERT_TRUE(lessEq(Point(1,1+half_eps,1),Point(1,1,1)));
+ ASSERT_TRUE(lessEq(Point(1,1,1+half_eps),Point(1,1,1)));
+ ASSERT_TRUE(lessEq(Point(1,1,1),Point(1+half_eps,1,1)));
+ ASSERT_TRUE(lessEq(Point(1,1,1),Point(1,1+half_eps,1)));
+ ASSERT_TRUE(lessEq(Point(1,1,1),Point(1,1,1+half_eps)));
+
+ ASSERT_TRUE(lessEq(Point(1-half_eps,1,1),Point(1,1,1)));
+ ASSERT_TRUE(lessEq(Point(1,1-half_eps,1),Point(1,1,1)));
+ ASSERT_TRUE(lessEq(Point(1,1,1-half_eps),Point(1,1,1)));
+ ASSERT_TRUE(lessEq(Point(1,1,1),Point(1-half_eps,1,1)));
+ ASSERT_TRUE(lessEq(Point(1,1,1),Point(1,1-half_eps,1)));
+ ASSERT_TRUE(lessEq(Point(1,1,1),Point(1,1,1-half_eps)));
+
+ const double m(std::numeric_limits<double>::min());
+ ASSERT_TRUE(lessEq(Point(m+half_eps,m,m),Point(m,m,m)));
+ ASSERT_TRUE(lessEq(Point(m,m+half_eps,m),Point(m,m,m)));
+ ASSERT_TRUE(lessEq(Point(m,m,m+half_eps),Point(m,m,m)));
+ ASSERT_TRUE(lessEq(Point(m,m,m),Point(m+half_eps,m,m)));
+ ASSERT_TRUE(lessEq(Point(m,m,m),Point(m,m+half_eps,m)));
+ ASSERT_TRUE(lessEq(Point(m,m,m),Point(m,m,m+half_eps)));
+
+ const double zero(0.0);
+ ASSERT_TRUE(lessEq(Point(zero+half_eps,zero,zero),Point(zero,zero,zero)));
+ ASSERT_TRUE(lessEq(Point(zero,zero+half_eps,zero),Point(zero,zero,zero)));
+ ASSERT_TRUE(lessEq(Point(zero,zero,zero+half_eps),Point(zero,zero,zero)));
+ ASSERT_TRUE(lessEq(Point(zero,zero,zero),Point(zero+half_eps,zero,zero)));
+ ASSERT_TRUE(lessEq(Point(zero,zero,zero),Point(zero,zero+half_eps,zero)));
+ ASSERT_TRUE(lessEq(Point(zero,zero,zero),Point(zero,zero,zero+half_eps)));
+
+ ASSERT_TRUE(lessEq(Point(m+half_eps,m,m),Point(zero,zero,zero)));
+ ASSERT_TRUE(lessEq(Point(m,m+half_eps,m),Point(zero,zero,zero)));
+ ASSERT_TRUE(lessEq(Point(m,m,m+half_eps),Point(zero,zero,zero)));
+ ASSERT_TRUE(lessEq(Point(m,m,m),Point(zero+half_eps,zero,zero)));
+ ASSERT_TRUE(lessEq(Point(m,m,m),Point(zero,zero+half_eps,zero)));
+ ASSERT_TRUE(lessEq(Point(m,m,m),Point(zero,zero,zero+half_eps)));
+
+ ASSERT_TRUE(lessEq(Point(zero+half_eps,zero,zero),Point(m,m,m)));
+ ASSERT_TRUE(lessEq(Point(zero,zero+half_eps,zero),Point(m,m,m)));
+ ASSERT_TRUE(lessEq(Point(zero,zero,zero+half_eps),Point(m,m,m)));
+ ASSERT_TRUE(lessEq(Point(zero,zero,zero),Point(m+half_eps,m,m)));
+ ASSERT_TRUE(lessEq(Point(zero,zero,zero),Point(m,m+half_eps,m)));
+ ASSERT_TRUE(lessEq(Point(zero,zero,zero),Point(m,m,m+half_eps)));
+
+ ASSERT_TRUE(lessEq(Point(half_eps+half_eps,half_eps,half_eps),Point(half_eps,half_eps,half_eps)));
+ ASSERT_TRUE(lessEq(Point(half_eps,half_eps+half_eps,zero),Point(half_eps,half_eps,half_eps)));
+ ASSERT_TRUE(lessEq(Point(zero,zero,zero+half_eps),Point(half_eps,half_eps,half_eps)));
+ ASSERT_TRUE(lessEq(Point(half_eps,half_eps,half_eps),Point(half_eps+half_eps,half_eps,half_eps)));
+ ASSERT_TRUE(lessEq(Point(half_eps,half_eps,half_eps),Point(half_eps,half_eps+half_eps,half_eps)));
+ ASSERT_TRUE(lessEq(Point(half_eps,half_eps,half_eps),Point(half_eps,half_eps,half_eps+half_eps)));
+
+ ASSERT_TRUE(lessEq(Point(10.0+half_eps,10.0,10.0),Point(10.0,10.0,10.0)));
+ ASSERT_TRUE(lessEq(Point(10.0,10.0+half_eps,10.0),Point(10.0,10.0,10.0)));
+ ASSERT_TRUE(lessEq(Point(10.0,10.0,10.0+half_eps),Point(10.0,10.0,10.0)));
+ ASSERT_TRUE(lessEq(Point(10.0,10.0,10.0),Point(10.0+half_eps,10.0,10.0)));
+ ASSERT_TRUE(lessEq(Point(10.0,10.0,10.0),Point(10.0,10.0+half_eps,10.0)));
+ ASSERT_TRUE(lessEq(Point(10.0,10.0,10.0),Point(10.0,10.0,10.0+half_eps)));
+}
+
+TEST(GeoLib, PointComparisonOperatorLessEq)
+{
+ const double my_eps(std::numeric_limits<double>::epsilon());
+ ASSERT_FALSE(Point(1.0+my_eps,1.0,1.0) <= Point(1.0,1.0,1.0));
+ ASSERT_FALSE(Point(1.0,1.0+my_eps,1.0) <= Point(1.0,1.0,1.0));
+ ASSERT_FALSE(Point(1.0,1.0,1.0+my_eps) <= Point(1.0,1.0,1.0));
+ ASSERT_TRUE(Point(1.0,1.0,1.0) <= Point(1.0+my_eps,1.0,1.0));
+ ASSERT_TRUE(Point(1.0,1.0,1.0) <= Point(1.0,1.0+my_eps,1.0));
+ ASSERT_TRUE(Point(1.0,1.0,1.0) <= Point(1.0,1.0,1.0+my_eps));
+
+ ASSERT_TRUE(Point(1.0-my_eps,1.0,1.0) <= Point(1.0,1.0,1.0));
+ ASSERT_TRUE(Point(1.0,1.0-my_eps,1.0) <= Point(1.0,1.0,1.0));
+ ASSERT_TRUE(Point(1.0,1.0,1.0-my_eps) <= Point(1.0,1.0,1.0));
+ ASSERT_FALSE(Point(1.0,1.0,1.0) <= Point(1.0-my_eps,1.0,1.0));
+ ASSERT_FALSE(Point(1.0,1.0,1.0) <= Point(1.0,1.0-my_eps,1.0));
+ ASSERT_FALSE(Point(1.0,1.0,1.0) <= Point(1.0,1.0,1.0-my_eps));
+
+ std::size_t n(10000);
+ srand ( time(NULL) );
+ for (std::size_t k(0); k<n; ++k) {
+ double random_val_x(((double)(rand()) / RAND_MAX - 0.5)); //real_dist(rng));
+ double random_val_y(((double)(rand()) / RAND_MAX - 0.5)); //real_dist(rng));
+ double random_val_z(((double)(rand()) / RAND_MAX - 0.5)); //real_dist(rng));
+
+ double big_x(random_val_x * std::numeric_limits<double>::max());
+ double big_y(random_val_y * std::numeric_limits<double>::max());
+ double big_z(random_val_z * std::numeric_limits<double>::max());
+
+ ASSERT_TRUE(Point(big_x-my_eps,big_y,big_z) <= Point(big_x,big_y,big_z));
+ ASSERT_TRUE(Point(big_x,big_y-my_eps,big_z) <= Point(big_x,big_y,big_z));
+ ASSERT_TRUE(Point(big_x,big_y,big_z-my_eps) <= Point(big_x,big_y,big_z));
+
+ ASSERT_TRUE(Point(big_x-my_eps,big_y-my_eps,big_z) <= Point(big_x,big_y,big_z));
+ ASSERT_TRUE(Point(big_x-my_eps,big_y,big_z-my_eps) <= Point(big_x,big_y,big_z));
+ ASSERT_TRUE(Point(big_x,big_y-my_eps,big_z-my_eps) <= Point(big_x,big_y,big_z));
+
+ ASSERT_TRUE(Point(big_x-my_eps,big_y-my_eps,big_z-my_eps) <= Point(big_x,big_y,big_z));
+
+ double small_x(random_val_x * std::numeric_limits<double>::epsilon());
+ double small_y(random_val_y * std::numeric_limits<double>::epsilon());
+ double small_z(random_val_z * std::numeric_limits<double>::epsilon());
+
+ ASSERT_TRUE(Point(small_x-my_eps,small_y,small_z) <= Point(small_x,small_y,small_z));
+ ASSERT_TRUE(Point(small_x,small_y-my_eps,small_z) <= Point(small_x,small_y,small_z));
+ ASSERT_TRUE(Point(small_x,small_y,small_z-my_eps) <= Point(small_x,small_y,small_z));
+
+ ASSERT_TRUE(Point(small_x-my_eps,small_y-my_eps,small_z) <= Point(small_x,small_y,small_z));
+ ASSERT_TRUE(Point(small_x-my_eps,small_y,small_z-my_eps) <= Point(small_x,small_y,small_z));
+ ASSERT_TRUE(Point(small_x,small_y-my_eps,small_z-my_eps) <= Point(small_x,small_y,small_z));
+
+ ASSERT_TRUE(Point(small_x-my_eps,small_y-my_eps,small_z-my_eps) <= Point(small_x,small_y,small_z));
+ }
+}