Intersection of vector and triangle side

In summary, the intersection of a vector and a triangle side is the point at which the vector and the side of the triangle meet. It can be calculated using the formula P = P0 + t(P1 - P0), and it is possible for the intersection point to be outside of the triangle. This point represents the contact or overlap between the two objects and has various real-world applications in computer graphics, navigation systems, and physics simulations.
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virusys
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Homework Statement



I have a triangle with given vertices ABC. Given a vector that starts from A and intersects side BC, how can I find the point of intersection, p?

vqX7x.png


Thanks


Homework Equations





The Attempt at a Solution

 
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welcome to pf!

hi virusys! welcome to pf! :smile:

find the two coordinate equations of the red line and of the line BC, and solve them as a pair of simultaneous equations :wink:
 

1. What is the definition of the intersection of a vector and a triangle side?

The intersection of a vector and a triangle side is the point at which the vector and the side of the triangle meet. It is the point of contact between the two objects.

2. How do you calculate the intersection point of a vector and a triangle side?

To calculate the intersection point, you can use the formula: P = P0 + t(P1 - P0), where P0 is the starting point of the vector, P1 is the end point of the vector, and t is the parameter that determines the position of the intersection point along the vector.

3. Can the intersection point of a vector and a triangle side be outside of the triangle?

Yes, it is possible for the intersection point to be outside of the triangle. This can happen if the vector is extended beyond the triangle's boundaries.

4. What does the intersection of a vector and a triangle side represent?

The intersection of a vector and a triangle side represents the point of contact or overlap between the two objects. It can also represent the direction in which the vector is moving towards the triangle side.

5. How can the intersection of a vector and a triangle side be used in real-world applications?

The intersection of a vector and a triangle side can be used in various applications, such as computer graphics, navigation systems, and physics simulations. For example, in computer graphics, it can be used to determine the location of a ray of light as it hits a surface of a 3D object. In navigation systems, it can be used to calculate the shortest distance between a moving object and a stationary object. In physics simulations, it can be used to determine the path of a moving object as it interacts with other objects in the simulation.

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