Which approach is used in the solution to check if point is in a triangle?

Question

1.00/5 (2 votes)

See more:

(Geometry: points in triangle?) Suppose a right triangle is placed in a plane as shown below. The right-angle point is placed at (0, 0), and the other two points are placed at (200, 0) and (0, 100). Write a program that prompts the user to enter a point with x- and y-coordinates and determines whether the point is inside the triangle.

Though there are many algorithms for this question. I was specifically concerned about the following one:

Java

System.out.println("Enter a point's x- and y-coordinates: ");
       double x = in.nextDouble();
       double y = in.nextDouble();

       double x1 = 0, y1 = 0, x2 = 200, y2 = 0,
              x3 = 0, y3 = 100; //Vertex coordinates for the given triangle

       double Dx, Dy, minD, maxD;

       String result = "";
       double determinant = (y2 - y3) * (x1 - x3) - (x3 - x2) * (y3 - y1);
       minD = Math.min(determinant, 0);
       maxD = Math.max(determinant, 0);
       Dx = x - x3;
       Dy = y - y3;

       double a = y2 - y3 * Dx + (x3 - x2) * Dy;
       if (a < minD || a > maxD) {
           result += "The point is not in the triangle.";
       }
       double b = (y3 - y1) * Dx + (x1 - x3) * Dy;
       if (b < minD || b > maxD) {
           result += "The point is not in the triangle.";
       }
       double c = determinant - a - b;
       if (c < minD || c > maxD) {
           result += "The point is not in the triangle.";

       } else {
           result += "The point is in the triangle.";
       }
       System.out.println(result);

Could anyone kindly take his/her time to explain this?

What I have tried:

I have tried areas comparison approach enclosed b/w the subtriangles and the main triangle. And cross vector product approach. I understood both.

Posted 4-Oct-23 1:21am

Unknown Boy 2023

Updated 4-Oct-23 3:02am

Deeksha Shenoy

v2

Add a Solution

Comments

Richard MacCutchan 4-Oct-23 8:29am

"time to explain this?"
You should ask the person who wrote it.

Unknown Boy 2023 4-Oct-23 8:44am

Man I found it on github. If you can't explain after my humble request than at least you can tell me about the method used here?

Richard MacCutchan 4-Oct-23 9:32am

I have never seen that code before so how do you expect me, or anyone else here, to explain it. If you find code on the internet then make sure you understand it before you decide to download it.

2 solutions

Add a Solution

Add your solution here

Treat my content as plain text, not as HTML

Preview 0

…

Existing Members

Sign in to your account

...or Join us

Download, Vote, Comment, Publish.

Your Email
Password
Forgot your password?

Your Email
This email is in use. Do you need your password?
Optional Password

I have read and agree to the Terms of Service and Privacy Policy
Please subscribe me to the CodeProject newsletters

When answering a question please:

Read the question carefully.
Understand that English isn't everyone's first language so be lenient of bad spelling and grammar.
If a question is poorly phrased then either ask for clarification, ignore it, or edit the question and fix the problem. Insults are not welcome.
Don't tell someone to read the manual. Chances are they have and don't get it. Provide an answer or move on to the next question.

Let's work to help developers, not make them feel stupid.

This content, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)

OriginalGriff · Answer 1 · 2023-10-04T02:50:00

Do you have any idea how much work explaining code line by line is?
Every single line needs a paragraph of explanation! For example:

int next = r.Next();

Create a new variable called "next" which can hold a integer value. From the previously declared Random instance "r", call the "Next" method to get a new random number, and assign it to the "next" variable.

Can you imagine how long it would take us to explain even a very short code fragment like your example, line by line?

No. It is not going to happen. If you have a specific problem, then ask a question about it. But think first - would you want to sit down for 45 minutes and type up a line-by-line description for no good reason?

tour belitung · Answer 2 · 2023-10-12T21:57:00

To check if a point is inside a triangle, there are several approaches you can use. One commonly used method is the "Barycentric Coordinate System" approach. Barycentric coordinates represent a point as a weighted sum of the vertices of the triangle. Here's how it works:

Calculate the Barycentric Coordinates:
Given a triangle with vertices A, B, and C and a point P that you want to check, you can calculate the Barycentric coordinates (u, v, w) of point P with respect to the triangle ABC using the following formulas:

u = ((v1.y - v2.y) * (p.x - v2.x) + (v2.x - v1.x) * (p.y - v2.y)) /
((v1.y - v2.y) * (v0.x - v2.x) + (v2.x - v1.x) * (v0.y - v2.y))

v = ((v2.y - v0.y) * (p.x - v2.x) + (v0.x - v2.x) * (p.y - v2.y)) /
((v1.y - v2.y) * (v0.x - v2.x) + (v2.x - v1.x) * (v0.y - v2.y))

w = 1 - u - v

Where (v0, v1, v2) are the vertices of the triangle, (p.x, p.y) is the point you want to check, and (u, v, w) are the Barycentric coordinates.

Check the Barycentric Coordinates:
If all the Barycentric coordinates (u, v, w) are between 0 and 1 (inclusive), it means that the point P is inside the triangle. If any of the coordinates are outside this range, the point is outside the triangle.

Here's a simple Java code example to check if a point is inside a triangle using the Barycentric Coordinate System:

public class PointInTriangle {
public static boolean isPointInTriangle(Point v0, Point v1, Point v2, Point p) {
double u = ((v1.y - v2.y) * (p.x - v2.x) + (v2.x - v1.x) * (p.y - v2.y)) /
((v1.y - v2.y) * (v0.x - v2.x) + (v2.x - v1.x) * (v0.y - v2.y));
double v = ((v2.y - v0.y) * (p.x - v2.x) + (v0.x - v2.x) * (p.y - v2.y)) /
((v1.y - v2.y) * (v0.x - v2.x) + (v2.x - v1.x) * (v0.y - v2.y));
double w = 1 - u - v;

return u >= 0 && v >= 0 && w >= 0 && u <= 1 && v <= 1 && w <= 1;
}

public static void main(String[] args) {
Point v0 = new Point(0, 0);
Point v1 = new Point(1, 0);
Point v2 = new Point(0, 1);
Point p = new Point(0.5, 0.5);

if (isPointInTriangle(v0, v1, v2, p)) {
System.out.println("Point is inside the triangle.");
} else {
System.out.println("Point is outside the triangle.");
}
}
}

class Point {
double x;
double y;

public Point(double x, double y) {
this.x = x;
this.y = y;
}
}

In this example, we define the isPointInTriangle method to check if a point is inside a triangle. You can use this method to determine whether a point lies inside a given triangle defined by its vertices.

Which approach is used in the solution to check if point is in a triangle?

2 solutions

Solution 1

Solution 3

Add your solution here

Preview 0