Find if a point is within a triangle: Difference between revisions
Find if a point is within a triangle (view source)
Revision as of 00:05, 12 January 2021
, 3 years ago→{{header|Factor}}
Line 135:
Triangle is [(0.100000, 0.111111), (12.500000, 33.333333), (-12.500000, 16.666667)]
Point (5.414286, 14.349206) is within triangle? true</pre>
=={{header|C++}}==
{{trans|C}}
<lang cpp>#include <iostream>
const double EPS = 0.001;
const double EPS_SQUARE = EPS * EPS;
double side(double x1, double y1, double x2, double y2, double x, double y) {
return (y2 - y1) * (x - x1) + (-x2 + x1) * (y - y1);
}
bool naivePointInTriangle(double x1, double y1, double x2, double y2, double x3, double y3, double x, double y) {
double checkSide1 = side(x1, y1, x2, y2, x, y) >= 0;
double checkSide2 = side(x2, y2, x3, y3, x, y) >= 0;
double checkSide3 = side(x3, y3, x1, y1, x, y) >= 0;
return checkSide1 && checkSide2 && checkSide3;
}
bool pointInTriangleBoundingBox(double x1, double y1, double x2, double y2, double x3, double y3, double x, double y) {
double xMin = std::min(x1, std::min(x2, x3)) - EPS;
double xMax = std::max(x1, std::max(x2, x3)) + EPS;
double yMin = std::min(y1, std::min(y2, y3)) - EPS;
double yMax = std::max(y1, std::max(y2, y3)) + EPS;
return !(x < xMin || xMax < x || y < yMin || yMax < y);
}
double distanceSquarePointToSegment(double x1, double y1, double x2, double y2, double x, double y) {
double p1_p2_squareLength = (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);
double dotProduct = ((x - x1) * (x2 - x1) + (y - y1) * (y2 - y1)) / p1_p2_squareLength;
if (dotProduct < 0) {
return (x - x1) * (x - x1) + (y - y1) * (y - y1);
} else if (dotProduct <= 1) {
double p_p1_squareLength = (x1 - x) * (x1 - x) + (y1 - y) * (y1 - y);
return p_p1_squareLength - dotProduct * dotProduct * p1_p2_squareLength;
} else {
return (x - x2) * (x - x2) + (y - y2) * (y - y2);
}
}
bool accuratePointInTriangle(double x1, double y1, double x2, double y2, double x3, double y3, double x, double y) {
if (!pointInTriangleBoundingBox(x1, y1, x2, y2, x3, y3, x, y)) {
return false;
}
if (naivePointInTriangle(x1, y1, x2, y2, x3, y3, x, y)) {
return true;
}
if (distanceSquarePointToSegment(x1, y1, x2, y2, x, y) <= EPS_SQUARE) {
return true;
}
if (distanceSquarePointToSegment(x2, y2, x3, y3, x, y) <= EPS_SQUARE) {
return true;
}
if (distanceSquarePointToSegment(x3, y3, x1, y1, x, y) <= EPS_SQUARE) {
return true;
}
return false;
}
void printPoint(double x, double y) {
std::cout << '(' << x << ", " << y << ')';
}
void printTriangle(double x1, double y1, double x2, double y2, double x3, double y3) {
std::cout << "Triangle is [";
printPoint(x1, y1);
std::cout << ", ";
printPoint(x2, y2);
std::cout << ", ";
printPoint(x3, y3);
std::cout << "]\n";
}
void test(double x1, double y1, double x2, double y2, double x3, double y3, double x, double y) {
printTriangle(x1, y1, x2, y2, x3, y3);
std::cout << "Point ";
printPoint(x, y);
std::cout << " is within triangle? ";
if (accuratePointInTriangle(x1, y1, x2, y2, x3, y3, x, y)) {
std::cout << "true\n";
} else {
std::cout << "false\n";
}
}
int main() {
test(1.5, 2.4, 5.1, -3.1, -3.8, 1.2, 0, 0);
test(1.5, 2.4, 5.1, -3.1, -3.8, 1.2, 0, 1);
test(1.5, 2.4, 5.1, -3.1, -3.8, 1.2, 3, 1);
std::cout << '\n';
test(0.1, 0.1111111111111111, 12.5, 33.333333333333336, 25, 11.11111111111111, 5.414285714285714, 14.349206349206348);
std::cout << '\n';
test(0.1, 0.1111111111111111, 12.5, 33.333333333333336, -12.5, 16.666666666666668, 5.414285714285714, 14.349206349206348);
std::cout << '\n';
return 0;
}</lang>
{{out}}
<pre>Triangle is [(1.5, 2.4), (5.1, -3.1), (-3.8, 1.2)]
Point (0, 0) is within triangle? true
Triangle is [(1.5, 2.4), (5.1, -3.1), (-3.8, 1.2)]
Point (0, 1) is within triangle? true
Triangle is [(1.5, 2.4), (5.1, -3.1), (-3.8, 1.2)]
Point (3, 1) is within triangle? false
Triangle is [(0.1, 0.111111), (12.5, 33.3333), (25, 11.1111)]
Point (5.41429, 14.3492) is within triangle? true
Triangle is [(0.1, 0.111111), (12.5, 33.3333), (-12.5, 16.6667)]
Point (5.41429, 14.3492) is within triangle? true</pre>
=={{header|Factor}}==
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