All questions with tag [math: 3d]


Equation of a parabola-shaped toroidal tube with circular cross-sections

I require an implied function that stories the surface area that I am revealing you aware. Every little thing you require is revealed there. The surface area is a tube in the form of a parabola. The distance of its cross - areas is $3$.
2022-07-25 17:16:00

How to calculate distance between point and object in 3d space

I have object in 3d room developed from factors $P_i(x, y, z)$ where I can create triangulars, and also I require to calulate range from factor X to this object. I attempt to take 3 factors from tiniest range and also calulate elevation of tetrahedron developed from this 3 factors and also X , yet this will certainly be not the range from the ...
2022-07-25 13:22:02

Finding the distance between the centre of an arbitrarily rotated cylinder and a point on that cylinder

this is a little bit extra difficult than the blog post title recommends due to the fact that I was lacking words. I intend the complete title would certainly be: "Finding the range in between the centre of a randomly revolved cyndrical tube and also a factor on that particular cyndrical tube which is the junction of a ray predicted from th...
2022-07-25 12:49:49

Periodical reflection conditions in a sphere.

An excellent mirror covered the within surface area of a round (presumption: there is no any kind of loss throughout representation and also representations proceed countless) and also there is a really tiny laser on factor $A$ in the surface area of the round and also the instructions of the laser light mosts likely to within and also mirrors f...
2022-07-25 12:36:17

Analytic caustics for 3D objects

Is it feasible to successfully compute caustics for an offered 3D object, like a torus, or a dice? To be extra specific: allow is think that we have a 3d torus, hing on a 2d aircraft and also a solitary source of light, sending out light in all instructions. Exists an "efficient" (polynomial) algorithm for calculating the strength of ...
2022-07-25 12:25:52

Calculating angle of human joint beyond 180° in 3D

I'm having some problem computing the angle of an human joint in 3D making use of the Microsoft Kinect. Below is an instance of the angle of the joint (making use of the shoulder and also wrist joint) : Image of exampleComputing angles in between 0° and also 180° is no worry, yet when the individual active expands his joint my estimation return...
2022-07-25 07:44:53

3-D equation of a circle

I found an amount yet can not address it as i do not recognize the 3d formulas of a circle: ¢ The amount is If $A(3,-2,2)$ and also $B(2,9,5)$ are completion factors of a size of a circle, after that the 3rd pt that pushes the circle is $5,6,1$ $5,6,-1$ $5,-6,1$ $-5,-6,-1$ Ans: 2 Would value if a person can clarify the formula of a c...
2022-07-24 06:35:08

Icosahedron coordinates

Wikipedia claims (link) that cartesian works with of icosahedron are: (0, ±1, ± φ) (±1, ± φ, 0) (± φ, 0, ±1) Where φ = (1+√ 5) / 2 is gold proportion ≈ 1.618. I located on the net this code: // vertex position and color information for icosahedron vertices[0] = new VertexPositionColor(new Vector3(-0.26286500f, 0.0000000f, 0.425325...
2022-07-24 06:20:37

How to fly a curve from one heading to another using only roll and pitch.

I have 3 vertical vectors standing for an object in 3d room Heading Right Up and also I would love to have the ability to 'fly' this object to make sure that it winds up at a details factor and also heading making use of just roll and also pitch (no yaw) to make sure that the object adheres to a smooth flightpath. This is for spacecraf AI.
2022-07-22 15:02:12

Need to define an integral expression to find the area of intersection of a Plane and a Cone.

How can the indispensable expression be specified to locate Area (S) on $x+y+z=1$ and also surrounded with junction of the cone ($x^2+y^2-z^2=0$) and also the aircraft ($x+y+z=1$)?
2022-07-19 22:28:26

Determining angle of tilt from length of axes?

When taking an image of a cross, if the facility of the cross is recognized, exists any kind of means to establish the angle at which the image was taken based upon the variety of factors on the y axis over and also listed below the x axis? As an example, the line of the x axis is in between the factors (0,5) and also (10,5). The line of the y ...
2022-07-19 22:22:06

"Normalizing" Points on a Sphere

I have a set of points on a unit sphere representing different orientations: Now I need to apply rotation(s) such that the points will lay on the horizon as tightly as possible: The ideal representation for rotation would be YPR (Yaw-Pitch-Roll), but any axis-angle representation would suffice. Here is where I got up to now: Find "centro...
2022-07-19 22:14:35

Normal from multiple vectors

I have a several 3D vectors $X_{i}$ which lay approximately in a plane. Now I need to find a single vector, which is normal (as much as possible) to all of them. For two vectors, I can use a cross product to obtain such vector. For multiple vectors, I found this formula: $$\left( \sum_{i=1}^{n} X_{i}X_{i}^{\textbf{T}} \right)u=0$$ Here $u$ is th...
2022-07-19 21:59:12

Finding an equation of a sphere for a specific plane

I am not sure how to proceed with this question from Stewart's SV Calculus text: Find equations of the sphere's with center $(2, -3, 6)$ that touch (a) the $xy$-plane, (b) the $yz$-plane, (c) the $xz$-plane. I know that the equation for a sphere should look like this: $$(x - 2)^2 + (y + 3)^2 + (z - 6)^2 = r^2$$ But I am not sure how to sol...
2022-07-19 21:45:55

Should/do parallel lines curve when rendered with perspective?

Simple viewpoint estimations made use of in providing 3D factors onto a 2D screen take the kind of separating the electronic camera - loved one works with by range from electronic camera and also increasing by an area - of - sight parameter, as defined below: So if I have...
2022-07-17 14:40:47

How to calculate the area of a 3D triangle?

I have works with of 3d triangular and also I require to compute its area. I recognize just how to do it in 2D, yet do not recognize just how to compute area in 3d. I have actually created information as adheres to. (119.91227722167969, 122.7717056274414, 39.3568115234375), (119.8951187133789, 122.7717056274414, 39.38057327270508), (121.119415...
2022-07-17 14:17:07

Find P points inside ABCD tetrahedron so that volume of ABCP = volume of ABDP

Find all $P$ factors inside $ABCD$ tetrahedron, to make sure that $V_{ABCP} = V_{ABDP}$ Thanks beforehand for any kind of aid.
2022-07-17 14:01:27

What is the tangent plane equation on the 3 spheres?

3 rounds get on $z=0$ aircraft and also touch each various other as received the image. Coordinates of their facilities are $O_1=(0,0,5),O_2=(0,y_2,3),O_3=(x_3,y_3,2)$. What is the tangent aircraft formula on 3 rounds? ($ax+by+cz=d$) Thanks for solutions.
2022-07-17 12:12:14

Quaternions and spatial translations

From my understanding, in spatial applications (3D making, video games and also comparable applications) quaternions can just be made use of to define rotations/orientations and also not translations (like a makeover matrix does). This appears to be supported by the reality that the majority of 3D structures that make use of quaternions (OGRE3D...
2022-07-16 14:35:15

polygon inside a polygon

i have numerous factor spots push various planar faces. after that, I got confining polygons to stand for factors to make sure that i have numerous planar polygons (as an example A, B, C, D). when i check out the polygons, i located some polygons (B) lies inside an additional bigger polygon (A) yet at various elevation degree. additionally some ...
2022-07-16 14:27:00