What does Delta Z stand for? Can you give a definition? Is it like a derivative?laminatedevildoll said:Suppose that there is a rectangular plane in coordinates x,y and z is pointing out of the page. There are corners A,B,C,D. How do I find the delta Z of the at the midpoint of the plane. I know that the equation of a plane is A + Bx + Cy = D
Sorry, I should've been more clearer. This is a 3-D problem. There is a traingle in a cartesian plane, with sides A,B,C. Suppose I want to find out what z(x,y) (the midpoint between the rectangular plane with respect to x,y), I have to write the following equations...EnumaElish said:What does Delta Z stand for? Can you give a definition? Is it like a derivative?
Also, the plane equation does not include z, is that correct? Why are there two separate constants, A and D? What makes me curious is that if the equation didn't include a Z term, it would have been more economical to write it as A + Bx + Cy = 0; or one might write it as Bx + Cy = F (such that F = D - A in your notation).
How would you restate this problem on the Cartesian plane, a line replacing the plane? Since your plane equation does not involve the z coordinate, I am going to assume that the equivalent formula for the line does not include the y coordinate: Bx = D. How would you define delta Y (the equivalent of delta Z in your case) at the midpoint of the line?
I might be able to help if you give a little more explanation and/or redefine the problem as a line in the XY coordinates (Cartesian 2-dimensional plane) instead of a plane in the XYZ coordinates (Cartesian 3-dimensional space). Does this makes sense?
I should've said, "then you will have a general (or generic) formula that would represent the relationship between the (x, y) coordinates and the z coordinate ON THE OBJECT THAT THOSE 3 EQUATIONS ARE DESCRIBING." So if the 3 eq's describe a triangle then the generic eq. would also describe the same triangle in generic terms.myself said:... If you take these solutions (for ex., let's say you find A = 2, B = 0.5, C = -3) and plug them into the eq. for z(x,y) then you will have a general (or generic) formula that would represent the relationship between the (x, y) coordinates and the z coordinate.
Well, if I am writing a computer program, then I don't have number constants. Instead, I have to plug in and form equations in order to find the coefficients I guess. Is there any way, to calculate the slope of each side, right, left, top and bottom to determine delta z? Can I relate delta z to the slopes in any way. I am still experimenting a bit.EnumaElish said:The 3 equations will give you constants A, B, C assuming you have numbers (data) for xi, yi, zi for i = a, b, c (that is, delta z with respect to each side).
If you take these solutions (for ex., let's say you find A = 2, B = 0.5, C = -3) and plug them into the eq. for z(x,y) then you will have a general (or generic) formula that would represent the relationship between the (x, y) coordinates and the z coordinate.
Does this answer your Q?
Yes... the user will enter some coordinates.EnumaElish said:I hear you, but when it is time to run the program, will the user (running the prog.) going to have those inputs? Is each of these points an input to the prog.? Just trying to understand the context.
Yes, I suppose so. However, the question about the warped plane is behind me now. I have moved on to much better things.EnumaElish said:Is this somehow related to the warped plane question that has been posted under a different thread?
Yes, solve for A,B,C after knowing what [tex]\Delta Z_i[/tex] is, for i = a, b, c.laminatedevildoll (under another thread) said:I have a 3-D traingle, and the edges are a,b,c. ...
My equations are
[tex]\Delta Z[/tex] = A + Bx + Cy
[tex]\Delta Z_a[/tex] = A + Bx_a + Cy_a
[tex]\Delta Z_b[/tex] = A + Bx_b + Cy_b
[tex]\Delta Z_c[/tex] = A + Bx_c + Cy_c
In order to solve for [tex]\Delta Z[/tex], how do I use the above equations? Do I have to add them (equations 2,3,4) all up and substitute in A for the first equation?
To find the coefficients, do I just solve for A,B,C after I know what [tex]\Delta Z[/tex] is?
I see. I appreciate your help. I had initially had some sort of equations like that, except I had a 4 thrown somewhere in there. It's really strange how I have forgotten the easier concepts in Math. Old age, I presume.EnumaElish said:Yes, solve for A,B,C after knowing what [tex]\Delta Z_i[/tex] is, for i = a, b, c.
1st specific eq gives you A = z_a - Bx_a - Cy_a
Write 2nd eq as
z_b = z_a - Bx_a - Cy_a + Bx_b + Cy_b
z_b - z_a = B(x_b - x_a) + C(y_b - y_a)
B = ( (z_b - z_a) - C(y_b - y_a) )/(x_b - x_a)
Write 3rd eq as
z_c = z_a - Bx_a - Cy_a + Bx_c + Cy_c
z_c - z_a = B(x_c - x_a) + C(y_c - y_a)
z_c - z_a = (x_c - x_a)( (z_b - z_a) - C(y_b - y_a) )/(x_b - x_a) + C(y_c - y_a)
Solve for C.
Replace C in B.
Replace B and C in A.