Vector Calc Homework: Find Dv from Pr & Pt

In summary, to find the directional vector (Dv) for a GPS tracking system in a game, you need to use the equation Dv = (cos(atan(Y,X)-Yaw), sin(atan(Y,X)-Yaw)), where Theta is the angle between the Pr line and the Pt point, and Yaw is the direction the object is facing relative to the world.
  • #1
Alienufo736
1
0

Homework Statement


Im not sure where exactly i should post this, but I am going to assume its here. basicaly what i am working on is programming a GPS tracking system inside a game. i have two GPS coordinates, one of the object that will be moving towards a stationary gps, and a stationary "target" GPS. I've figured out that it will be two points on a plane, what i need is the equation to find Dv or the direction to the Target GPS from the object GPS relative to the direction the object is facing . I've drawn a picture to assist myself in finding out exactly what i need to do.
Triangulation2.jpg

Pr=Gps on object, the line that contains Pr represents the direction that the object is facing, Pt=Target Gps, Dv=Directional Vector, Theta = Angle to Pt, Ignore Dv+ and Dv- i simply put that there to say that one side of Pr will be negative and the other positive along Dv. what i need to know is how to get the value of Dv with an equation. The Large circle around Pr represents its rotational possibilities. Note Dv must always be perpendicular to the Line Pr is in (which represents the object)

2. The attempt at a solution
I think I've figured out how to get Theta, but i could be wrong:
X = Xr - Xt
Y = Yr - Yt
Theta = atan(Y,X)-Yaw

Yr and Yt being the Y values of Pr And Pt Respectively
Xr and Xt being the Y values of Pr And Pt Respectively
Yaw being the direction the object is facing relative to the world within -180 to 180 Degrees Any help would be appreciated, i hope i explained everything alright, if not, just ask, ill elaborate.
 
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  • #2
Homework EquationsX = Xr - XtY = Yr - YtTheta = atan(Y,X)-YawThe AnswerThe equation you need to calculate the directional vector (Dv) is:Dv = (cos(Theta), sin(Theta))Where Theta is the angle between the Pr line and the Pt point, which you have calculated as:Theta = atan(Y,X)-YawTherefore, the equation for the directional vector (Dv) is:Dv = (cos(atan(Y,X)-Yaw), sin(atan(Y,X)-Yaw))
 
  • #3


Hello,

Thank you for reaching out for assistance with your vector calculus homework. It sounds like you are working on a very interesting project involving GPS tracking within a game. Let me try to help you with your question.

First, it is important to note that the directional vector Dv will depend on the orientation of the object and its position relative to the target GPS. To find Dv, we need to use vector subtraction. This means taking the coordinates of the target GPS (Pt) and subtracting the coordinates of the object GPS (Pr).

Dv = Pt - Pr

This will give you the directional vector from the object GPS to the target GPS. However, as you mentioned, you also need to take into account the orientation of the object. To do this, we need to use the concept of dot product.

The dot product of two vectors is given by:

A · B = |A||B|cos(θ)

Where A and B are vectors, |A| and |B| are the magnitudes of A and B, and θ is the angle between the two vectors.

In your case, A represents the directional vector Dv and B represents the direction in which the object is facing, which you have labeled as Pr. The dot product will give you the magnitude of Dv in the direction of Pr. To get the full directional vector, we then need to multiply this magnitude by the unit vector in the direction of Pr.

Dv = (|Dv|cos(θ)) * (Pr/|Pr|)

This will give you the full directional vector Dv, which will always be perpendicular to the direction in which the object is facing. It is important to note that the magnitude of Dv will depend on the distance between the object and the target GPS, as well as the angle between the two.

I hope this helps clarify things for you and provides you with a solution to your homework problem. If you have any further questions, please don't hesitate to ask. Good luck with your project!
 

Related to Vector Calc Homework: Find Dv from Pr & Pt

What is Vector Calc Homework?

Vector Calc Homework is a type of assignment that involves the use of vector calculus, a branch of mathematics that deals with vectors and their properties, to solve problems related to physics and engineering.

What does "Find Dv from Pr & Pt" mean?

"Find Dv from Pr & Pt" is a common notation used in vector calculus problems. It means to find the derivative of a vector, Dv, from the position vector, Pr, and the time vector, Pt.

Why is finding Dv from Pr & Pt important?

Finding Dv from Pr & Pt is important because it allows us to determine the rate of change of a vector with respect to time. This is crucial in many real-world applications, such as predicting the motion of objects, analyzing fluid flow, and understanding electromagnetic fields.

What are some common techniques used to find Dv from Pr & Pt?

Some common techniques used to find Dv from Pr & Pt include using the chain rule, product rule, quotient rule, and the derivative rules for vector functions. These techniques are based on the fundamental principles of calculus and can be applied to different types of vector calculus problems.

Are there any resources available to help with Vector Calc Homework?

Yes, there are many resources available to help with Vector Calc Homework. These include textbooks, online tutorials, practice problems, and forums where students can ask for help and clarification. It is also helpful to consult with a tutor or professor for additional support and guidance.

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