I need a geometric math formula solved
€30-250 EUR
Betalt ved levering
Say I have
- a sphere with a center and a radius
- the center of the sphere is moving along a line
- So it has the position x1 at time 0 and the position x2 at the time t2
- So x(t)=(1-t)*x1 + t*x2
And I have
- a plane
- that is defined by a normal vector n1 and a point on the plane p1 at time 0
- the plane now rotates/moves into a new position p2 and orientation n2 (given as a normal vector) at time t2
- there is a formula for the rotation called Rodriguez formula which quite nicely interpolates the rotational motion ([login to view URL])
- the plane's translation is p(t)=(1-t)*p1 + t*p2
- I am looking for a formula for the time between 0 and t2, when the plane and the sphere collide (All the positions and vectors are in 3d space)?
I have a Maple file and a Python(sympy) file, that might help you. I tried to solve it myself, but calling the solve function doesn't seem to finish.
Addendum
-----------------
This is the intersection formula for the plane and the sphere:
Let's say that specific aspects of this situation are time dependent:
x(t): the position of the sphere center at time t
p(t): the position of one point on the plane at time t
n(t): the orientation of the plane at time t
Then we can write the plane as an equation:
Y: any point on the plane
the normal vector is perpendicular to the vector between two points on the plane
( Y - p(t) ) · n(t) = 0
this also applies to the unit normal vector
( Y - p(t) ) · n(t) / |n(t)|= 0
In this formula, you can plug in a point L which is not on the plane, and in return, get the distance to this point instead of 0:
( L - p(t) ) · n(t) / |n(t)|= distance between L and plane
The point L is the position of the sphere center
( x(t) - p(t) ) · n(t) / |n(t)|= distance between sphere center and plane
The distance should be the radius of the sphere
( x(t) - p(t) ) · n(t) / |n(t)|= R
Simplify this a little
( x(t) - p(t) ) · n(t) = R · |n(t)|
Projekt ID: #30181210
Om projektet
Tildelt til:
Dear Sir. As an experienced algorithm expert, it is very interesting to me. I have been working on several data structure & algorithm projects such yours for over 7+ years. Since having programming contestant experienc Flere
11 freelancere byder i gennemsnit €103 timen for dette job
Hello, I hope this finds you well. I have just seen your project requiring; Engineering Matlab and Mathematica Mathematics Programming I believe that my 8-year experience in this field is what you need right away. Avo Flere
Hello I am hamami wessim and I am basically a math teacher and an IT engineer with several skills in matlab , python and statistics. I am very interested in your project and I am very motivated to render my service to Flere
.....................................................................................................................................................................................................expert here ..ping me
Hi; i can help you Now (immediately) send me a message so that we can discuss more. Thanks and regards.
AN EXPERT IN THE NAMED SKILLS, DEAR CLIENT, After KEENLY and PREFESSIONALLY reading your description and being in position to understand CLEARLY STATED REQUIRED SKILLS and is this one of my areas of PROFESSIONAL SPECIA Flere
I have completed mphil mathematics and I am interested in your project and I complete your project with hundred percent accuracy and within time
Hello there! I have just read your job description. I am very interested to work in your project. I will deliver the best quality work with 100% guaranty. I have knowledge of geometry andpython My skills include 3d mod Flere
Hi! I am skilled Python developer. I am familiar with Python and I have a lot of work experiences in Programming and Mathematics. I can start right away. I want to discuss for this project in detail. Please contact m Flere