If a 3D object has 4 points. why use x,y,z to describe 3D?

Thread starter Darken-Sol
Start date Apr 12, 2011
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3d Points

In summary: B, C, and D all move by three feet in the direction of A. However, the point E moves by four feet in the opposite direction. That's because the point E is offset from the tetrahedron's center. Indeed, it is possible to move in any direction by adding or subtracting coordinate points.

Apr 30, 2011

Darken-Sol

klackity said:

Darken-Sol: Did you not read my post about simplexes (the generalization of tetrahedrons)?

It's been done before. Here's a wikipedia article on exactly what I told you about: http://en.wikipedia.org/wiki/Barycentric_coordinate_system_(mathematics)

The wikipedia article uses linear algebra, but you can define Barycentric coordinates using compass and straightedge constructions (I think).

But I don't think anyone here is going to bother explaining the geometry to you.

i checked out a few links and bookmarked them. i only get about four hours a day to study, but now that its the weekend i'll go over them. this last one seems to be exactly what i was liiking for. i just read the first couple paragraphs then came back to express my appreciation for your time. thanks for the refocus.

<h2>1. Why do we need three coordinates (x,y,z) to describe a 3D object?</h2><p>The x,y,z coordinates represent the three dimensions of length, width, and height. In order to fully describe the position and orientation of a 3D object, we need to know its location in all three dimensions. This allows us to accurately define the shape and size of the object in space.</p><h2>2. Can't we just use two coordinates (x,y) to describe a 3D object?</h2><p>No, using only two coordinates would only give us information about the object's position in a 2D plane. In order to fully describe a 3D object, we need to know its position in all three dimensions. Using only two coordinates would not give us enough information to accurately represent the object's shape and size in space.</p><h2>3. How do the x,y,z coordinates relate to the dimensions of length, width, and height?</h2><p>The x,y,z coordinates correspond to the length, width, and height dimensions respectively. The x-axis represents the horizontal dimension (length), the y-axis represents the vertical dimension (height), and the z-axis represents the depth dimension (width).</p><h2>4. Why is it important to use a Cartesian coordinate system (x,y,z) for 3D objects?</h2><p>The Cartesian coordinate system is a standardized way of representing points in space. It allows for precise and consistent measurements and calculations of 3D objects. It also allows for easy visualization and manipulation of 3D objects in computer graphics and modeling.</p><h2>5. Can we use other coordinate systems besides Cartesian (x,y,z) to describe 3D objects?</h2><p>Yes, there are other coordinate systems that can be used to describe 3D objects, such as polar coordinates or spherical coordinates. However, the Cartesian coordinate system is the most commonly used and is often preferred for its simplicity and ease of use in mathematical calculations.</p>

1. Why do we need three coordinates (x,y,z) to describe a 3D object?

The x,y,z coordinates represent the three dimensions of length, width, and height. In order to fully describe the position and orientation of a 3D object, we need to know its location in all three dimensions. This allows us to accurately define the shape and size of the object in space.

2. Can't we just use two coordinates (x,y) to describe a 3D object?

No, using only two coordinates would only give us information about the object's position in a 2D plane. In order to fully describe a 3D object, we need to know its position in all three dimensions. Using only two coordinates would not give us enough information to accurately represent the object's shape and size in space.

3. How do the x,y,z coordinates relate to the dimensions of length, width, and height?

The x,y,z coordinates correspond to the length, width, and height dimensions respectively. The x-axis represents the horizontal dimension (length), the y-axis represents the vertical dimension (height), and the z-axis represents the depth dimension (width).

4. Why is it important to use a Cartesian coordinate system (x,y,z) for 3D objects?

The Cartesian coordinate system is a standardized way of representing points in space. It allows for precise and consistent measurements and calculations of 3D objects. It also allows for easy visualization and manipulation of 3D objects in computer graphics and modeling.

5. Can we use other coordinate systems besides Cartesian (x,y,z) to describe 3D objects?

Yes, there are other coordinate systems that can be used to describe 3D objects, such as polar coordinates or spherical coordinates. However, the Cartesian coordinate system is the most commonly used and is often preferred for its simplicity and ease of use in mathematical calculations.