Rectangular to spherical coordinate converter

RECTANGULAR TO SPHERICAL COORDINATE CONVERTER CODE

In other words, the Cartesian Del operator consists. In the diagram below, we see that the adjacent side is equal to the z component and the hypotenuse is equal to ПЃ. To convert it into the spherical coordinates, we have to convert the variables of the partial derivatives. The cosine is equal to the adjacent side divided by the hypotenuse. To find this angle, we can use the cosine function. This is the angle formed by the line and the positive z-axis. Quadrant Value of I We use the value of the calculator II We add 180В° to the calculator value III We add 180В° to the calculator value IV We add 360В° to the calculator valueДЇinally, we have the angle П†. This does not cover all four quadrants of the Cartesian plane, so we use the following table to correct this: However, we must bear in mind that the angle Оё given by the calculator is sometimes incorrect because the range of the inverse tangent function is to. The spherical coordinates system defines a point in 3D space using three parameters, which may be described as follows: The radial distance from the origin (O) to the point (P), r. This is a rather simple operation however it often results in some confusion. In the diagram, we can see that the opposite side is equal to the y component and the adjacent side is the x component. A common procedure when operating on 3D objects is the conversion between spherical and Cartesian co-ordinate systems. The tangent of an angle is equal to the opposite side divided by the adjacent side. We find this angle using the inverse tangent function. The angle Оё is the same as that found when transforming to cylindrical coordinates. Therefore, we have that ПЃ squared is equal to the sum of the squares of x, y, z: For this, we use the Pythagorean theorem in three dimensions. We can start by finding the length of ПЃ in terms of x, y, z. We can look at these components in the following diagram.

In this form, ПЃ is the distance from the origin to a three-dimensional point, Оё is the angle formed in the xy plane with respect to the x-axis, and П† is the angle formed with respect to the z-axis. We can transform from Cartesian coordinates to spherical coordinates using right triangles, trigonometry, and the Pythagorean theorem.Д¬artesian coordinates are written in the form ( x, y, z), while spherical coordinates have the form ( ПЃ, Оё, П†). If set, spherical coordinates are returned in a vector of the form, or a (3, n) array.How to transform from Cartesian coordinates to spherical coordinates? If set, rectangular coordinates are returned in a vector of the form or, or a (2, n) or (3, n) array. If set, polar coordinates are returned in a vector of the form, or a (2, n) array. If set, cylindrical coordinates are returned in a vector of the form, or a (3, n) array. FROM_SPHEREДЄ vector of the form, or a (3, n) array of spherical coordinates to convert.

FROM_RECTДЄ vector of the form or, or a (2, n) or (3, n) array containing rectangular coordinates to convert. FROM_POLARДЄ vector of the form, or a (2, n) array of polar coordinates to convert.

FROM_CYLINДЄ vector of the form, or a (3, n) array of cylindrical coordinates to convert. Set this keyword to force the computation to be done in double-precision arithmetic. If set, then the input and output coordinates are in degrees (where applicable). If none of the вЂњTO_вЂќ keywords are specified, the input coordinates are returned. To determine the spherical unit vectors in terms of cartesian. If none of the вЂњFROM_вЂќ keyword are specified, 0 is returned. We can use these expressions to convert spherical coordinates into cartesian and vice-versa. If the value specified in the вЂњFROM_вЂќ keyword is double precision, or if the DOUBLE keyword is set, then all calculations are performed in double precision and the returned value is double precision. Looking at Figure 2.98, it is easy to see that r sin. ExamplesД¬onvert from spherical to cylindrical coordinates: sph_coord =, ] rect_coord = CV_COORD(FROM_SPHERE=sph_coord, /TO_CYLIN, /DEGREES)Д¬onvert from rectangular to polar coordinates: rect_coord = polar_coord = CV_COORD(FROM_RECT=rect_coord, /TO_POLAR) Syntax The formulas to convert from spherical coordinates to rectangular coordinates may seem complex, but they are straightforward applications of trigonometry.

RECTANGULAR TO SPHERICAL COORDINATE CONVERTER CODE

Its source code can be found in the file cv_coord.pro in the lib subdirectory of the IDL distribution. This routine is written in the IDL language. This online application is capable of converting between three-dimensional Cartesian coordinates (x, y, z), spherical coordinates (r,, ) and cylindrical. The CV_COORD function converts 2D and 3D coordinates between the rectangular, polar, cylindrical, and spherical coordinate systems.

Rectangular to spherical coordinate converter