By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.

For a surface in 3D space, parametrization needs two parameters. You can use x, y as two parameters. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Calculating surface area of intersection between solid cylinder and plane Ask Question. Asked 4 years, 3 months ago. Active 3 months ago. Viewed 1k times. Michael Hardy k 27 27 gold badges silver badges bronze badges. Just add them at the end. Active Oldest Votes. Christian Blatter Christian Blatter k 12 12 gold badges silver badges bronze badges.

Narasimham Narasimham Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Featured on Meta.The surface area of a solid is a measure of the total area occupied by the surface of an object.

All of the objects addressed in this calculator are described in more detail on the Volume Calculator and Area Calculator pages. As such, this calculator will focus on the equations for calculating surface area the objects and the use of these equations.

Please refer to the aforementioned calculators for more detail on each individual object. Xael doesn't like sharing her chocolate truffles with anyone. When she receives a box of Lindt truffles, she proceeds to calculate the surface area of each truffle in order to determine the total surface area she has to lick to decrease the probability that anyone will try to eat her truffles.

Given that each truffle has a radius of 0. The surface area of a circular cone can be calculated by summing the surface area of each of its individual components. The "base SA" refers to the circle that comprises the base in a closed circular cone, while the lateral SA refers to the rest of the area of the cone between the base and its apex.

The equations to calculate each, as well as the total SA of a closed circular cone are shown below:. Athena has recently taken an interest in southeast Asian culture, and is particularly fascinated by the conical hat, typically referred to as a "rice hat," which is commonly used in a number of southeast Asian countries.

She decides to make one of her own, and being a very practical person not mired in sentimentality, retrieves her mother's wedding dress from the dark recesses of the wardrobe in which it resides. She determines the surface area of material she needs to create her hat with a radius of 1 foot and a height of 0. Anne wants to give her younger brother a Rubik's cube for his birthday, but knows that her brother has a short attention span and is easily frustrated.

She custom orders a Rubik's Cube in which all the faces are black, and has to pay for the customization based on the surface area of the cube with edge length of 4 inches.

The surface area of a closed cylinder can be calculated by summing the total areas of its base and lateral surface:. Jeremy has a large cylindrical fish tank that he bathes in because he doesn't like showers or bath tubs. He is curious whether his heated water cools faster than when in a bathtub, and needs to calculate the surface area of his cylindrical tank of height 5.

Banana, the eldest daughter of a long line of banana farmers, wants to teach her spoiled rotten little sister, Banana-Bread, a lesson about hope and expectations. Banana-Bread has been clamoring all week long about wanting a new set of drawers to house her new Batman action figures. As such, Banana buys her a large Barbie doll house with limited edition kitchen utensils, oven, apron, and realistic rotting bananas for Batman.

The surface area of a capsule can be determined by combining the surface area equations for a sphere and the lateral surface area of a cylinder. Note that the surface area of the bases of the cylinder is not included since it does not comprise part of the surface area of a capsule. The total surface area is calculated as follows:. He has already tested the market and has found that a vast majority of the sample population exhibit none of these qualities, and are very ready to purchase his product, further entrenching themselves within the traits they so desperately seek to escape.

Horatio needs to determine the surface area of each capsule so that he can coat them with an excessive layer of sugar and appeal to the sugar predisposed tongues of the population in preparation for his next placebo that "cures" all forms of diabetes mellitus.

Given each capsule has r of 0. The surface area of a spherical cap is based on the height of the segment in question.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. I have a tof camera pmd camboard nanoand my goal it's to between meshes calculate the distance from each other to calculate the deformation distance and the 3d position of specific points.

What is the best method to make that? I try with ruler, and euclidian distance in matlab with the point source, but i want the calcultion to be more precise. Here's a solution, assuming both datasets have exactly the same number of points and you are comparing point coordinates for points at the same index:.

The resulting dataset will have a result array which is the euclidean distance between the two corresponding points. To limit this calculation to specific points, you can use the Extract Selection or Threshold to extract smaller datasets with points of interest and then do the above.

Learn more. Asked 4 years, 9 months ago. Active 4 years, 9 months ago. Viewed 1k times. Active Oldest Votes. Here's a solution, assuming both datasets have exactly the same number of points and you are comparing point coordinates for points at the same index: Apply the Calculator filter on both the datasets separately with the expression coords. This will create new datasets with Result array in the PointData that corresponds to the point locations for each of the datasets.

Select the two calculator filters and then apply the Python Calculator filter with expression set to sqrt sum inputs[0]. PointData["Result"] - inputs[1]. Utkarsh Utkarsh 1, 1 1 gold badge 11 11 silver badges 19 19 bronze badges.

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The Overflow Bugs vs. How to put machine learning models into production. Featured on Meta.A, B, and C called attitude numbers are not all zero. The angle between two planes given by:.

Equation of a plane passing through 3 points P 1P 2P 3. Since the three points lies in the plane, each of them satisfies the plane equation:.

Any point on the intersection line between two planes satisfies both planes equations. This equations can be solved easyly by Cramer's rule. The intersection line can also be found by vector method. The general vector direction of the perpendicular lines to the first and second planes are the coefficients x, y and z of the planes equations. Note: any line can be presented by different values in the parametric equation.

There are two vectors extending from the origin to the other two points:. The cross product of this two vectors gives the general direction of the perpendicular vector to the plane, this is also the direction coefficients of the plane. All three points are located on the given plane,so each of the points satisfys the equation of the plane. We have two planes that is beacause they describe two planes tilted by 60 degrees either side of the given plane.

We have now three equations with four unknowns A, B, C and D theoretically there is no exact answer but we can solve the equations related to the unknown D. Another way to find the distance is by finding the plane and the line intersection point and then calculate distance between this point and the given point.

The distance between the given point and the plane is now the distance of the point to the intersection point and is given by the equation. Intersection of two planes and distance of a point to plane. Angle between plane 1 and plane 2 :. Intersection line parametric equation:. Plane defined by three points. Equation of a plane passing through 3 points:.

Plane defined by a point and a vector attitude numbers. Equation of a plane passing through the point:.But in this case we can use another method, which may be more useful: giving the coordinates of the points on the curve by expressions in some common variable called a "parameter" which may or may not be one of the coordinates. Roughly, what we expect is that a single equation in three variables determines a surface in space; two equations determine a curve or curves in the sense that the common solutions x,y of both equations form one or more curves ; and three dermine a point or isolated points.

And if we consider the infinitely many planes that all pass through the same line, then any two or more of their corresponding linear equations will still determine that common line. But "each new equation cuts down the dimension by one" is a handy rule of thumb. The real question is the more basic one: Is it true that the gradient is always perpendicular to the contour at its base?

Here is a piece of the original surface, with -2,2,-1 at one corner and with the above gradient vector drawn in dark green. The reader is invited to download the corresponding Winplot file and rotate it to see that gradient is indeed perpendicular to the surface. Let us suppose that we want to find all the points on this surface at which a vector normal to the surface is parallel to the yz -plane.

It is not clear, at least to me, that there are any such points; as I picture vectors perpendicular to the surface, they all seem to go forward or backward, at least slightly. But let us see what calculus tells us. So the desired points are on both the original surface and the new surface determined by this new equation shown in blue to the right.

Those points are arranged in two curves, drawn in green in this diagram.Given an incline with angle degrees which has a mass of kg placed upon it. There will be holes in the final surface anywhere at which etc.

Demonstrates how to calculate the intersection points between two user-specified curves. Detailed expanation is provided for each operation. Knowing the land elevation or altitude of land for a location can help you better plan a trip. Let's look at your second choice: "landing on a shaded portion and landing on a number greater than 3" Landing on a shaded portion would be 1 or 4.

In mathematical morph ology, the specimen is described by the set, S, of all the points contained within the specimen volume. Create an intersection between flat curves on the same plane. Because the strongest winds in a tropical cyclone are not located precisely at the center, it is possible for a cyclone's strongest winds to be experienced over land even if landfall does not occur. If the sphere center is outside the supercone, then the sphere and. Then, I found some geometry got triangle surface in it which didn't have before.

Use the angle marker on the side of the inclined plane to roughly set the angle. The blue points depict the detected intersection points.

### Finding the vector function for the curve of intersection of two surfaces

If two lines intersect, the sum of the resulting four angles equals I want to plot Cp along a section of this cylinder so I would like to chose the intersection of a normal plane and the wing surface to plot results on the resulting curve. If you were an Indianapolis race driver, you would use "slick" racing tires with no tread. To calculate the kite perimeter, you need to know two unequal sides.

Circle Theorems : Cyclic Quadrilateral Investigation; location spread shape.

Also, con- sider an object, A, that intersects only a por- tion of the ray. The three types of conic sections are the hyperbola, the parabola, and the ellipse. The above list is not all inclusive, but is intended to give typical examples of new construction or reconstruction work.

The Kitco Metal Quotes plugin allows you to calculate the volume of a selected Subtool and then receive cost estimates based on current Kitco. Now take a […]. Calculate the surface area.

The 'Surface Difference' geoprocessing tool can be used to calculate the geometric difference between two surfaces. Example As we see here something amazing happened.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information.

I am using ray tracing and at the beginning I assumed a plane surface so I used the equation of the plane surface which is :. My question now that I have function in matlab to read the surface of the object but the object may not be plane surface and I am getting the data of the surface [X Y Z] of the surface but I don't know which equation should I use to find t and then the intersection point.

And I even have a function to give me the normal vector at each point. If you can get the X Y Z of the surface and you said you can get the normal vector in each point so what is your problem now?

## intersection: surface-surface, curve-curve

The X Y Z of the surface are the intersection points and if you have the normal vector in each point so you can calculate whatever you want the reflected or the refracted rays. It might not be a plane, but you can always calculate a normal vector at each point. You'll just have to work harder to do it.

Take two partial derivatives in planar coordinates, cross those vectors, and that's the normal at the point. If your surface is defined as a height Z on a some X-Y grid, you can solve it easily using fzero. This would exclude some complex shapes, but might work for standard optics problems like a ray hitting a lens.

**Equation of Tangent Plane to a Surface at a Point Example #1**

Assume that XY and Z are 2-d matrices with the same shape. You can then do a 2d interpolation like. If this is not the case, you should try to define your own function that can calculate z based on x and y. So you can now define a function that calculates the height above the surface as a function of t as. Note that this might not be the shortest distance from the point to the plane, it is just the height measured along the z-direction.

The time the ray hits the surface can now be found by searching for the t for which the height is zero. This can be done for arbitrary functions using fzero :. This should work well for simple cases where the function defining the surface is relatively smooth and the ray crosses the surface only once. It might be possible to transform cases with more complex geometry into such a simple case.

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