Object and a 3d direction vector

In summary, a single 3D vector can determine a plane or a line, depending on the context. To determine if a point is below the plane determined by the vector, you can use the equation Ax+ By+ Cz< D, where the point's coordinates are substituted in for x, y, and z. If the resulting inequality is true, then the point is below the plane.
  • #1
badescuga
7
0
i have an object and a 3d direction vector and position for it . I would like to know how do i determine if a certain point X is in the space below the plan determined by my direction ?

Here is an image that i have drawn to make it more clear . In this image I've made the vector 2d

http://yfrog.com/53imgukp

Please Help!Regards,
Aleandru Badescu
 
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  • #2
Do you mean a "plane" or a "line"?

A single vector determines a line, Ax+ By= C, in two dimensions. A point (x,y) is on that line if y= (C- Ax)/B. It is "below" that line if y< (C- Ax)/B. If B is positive (and you can always arrange for B to be positive by multiplying the entire equation by -1 if necesary) that is the same as Ax+ By< C.

In three dimensions, a single vector <A, B, C>, determines a plane Ax+ By+ Cz< D. (x, y, z) is "below" that line if z< (D- Ax- By)/C. Again, if C is positive, that is the same as Ax+ By+ Cz< D.
 

Related to Object and a 3d direction vector

1. What is an object in relation to a 3d direction vector?

An object in a 3d space is a physical or virtual entity that has a position, orientation, and size. A 3d direction vector is a mathematical representation of a direction in 3-dimensional space, typically represented by three numerical values (x, y, z). In this context, an object can be located and oriented using a 3d direction vector.

2. How is a 3d direction vector represented?

A 3d direction vector is typically represented by three numerical values, known as components, which indicate the direction and magnitude in the x, y, and z axes. It can also be represented using mathematical notation such as d = (x, y, z).

3. What is the importance of a 3d direction vector in computer graphics?

A 3d direction vector is crucial in computer graphics as it allows for the representation of objects in a 3-dimensional space. It enables the manipulation of objects in 3d environments and is used in various algorithms for tasks such as rendering, lighting, and collision detection.

4. How is a 3d direction vector used in physics?

In physics, a 3d direction vector is used to represent the direction and magnitude of a physical quantity in 3-dimensional space. For example, in mechanics, a force can be represented by a 3d direction vector, where the components indicate the direction and magnitude of the force in the x, y, and z axes.

5. Can a 3d direction vector be normalized?

Yes, a 3d direction vector can be normalized, meaning its length is adjusted to 1 while preserving its direction. This is useful in various applications, such as in computer graphics, where normalized direction vectors are used for lighting calculations and in physics, where normalized vectors represent unit forces or velocities.

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