Скачать или смотреть Tangent to a sphere

Does a tangent plane touch a sphere at more than one point?


The simulation was realised with POV-Ray.

https://povray.org

The POV-Ray model is reported below and is released free for any use. The values of the variables that change dynamically during the simulation are given in the video in real-time for each individual frame.



//################# POV-Ray model file start ##################

#include "colors.inc"

// Units
#declare Km = 1; // kilometers units
#declare M = Km / 1000; // meters units
#declare Mi = 1609.344 * M; // miles unit
#declare Ft = Mi / 5280; // feet unit
#declare Yd = Mi / 1760; // yards unit
#declare NM = 1.852 * Km; // nautical miles unit

// Earth
#declare EarthRadius = 6371 * Km;
#declare EarthCheckerSquares = 4;
#declare CubeCheckerSquares = 4;

// Observer
#declare ObserverDist = 45000 * Km;
#declare ObserverAngle = 0 * Km;
#declare ObserverX = 0 * Km;
#declare ObserverY = 0 * Km;
#declare ZoomX = 1;
#declare ZoomY = 1;
#declare LookAtOrigin = 1;

// Reference point
#declare RefPointX = EarthRadius / CubeCheckerSquares;

#declare Rnd_1 = seed (1153);

// Derived variables
#declare EarthCenter = ＜0, -EarthRadius, 0＞;
#declare ObserverAngleRad = ObserverAngle * 2 * pi / 360;
#declare ObserverPos = ObserverDist * ＜sin(ObserverAngleRad), 0, cos(ObserverAngleRad)＞ + ＜ObserverX, ObserverY, 0＞;

#declare squaressize = function(Squares) { EarthRadius * 2 / Squares }
#declare EarthCheckerSquaresSize = squaressize(EarthCheckerSquares);
#declare CubeCheckerSquaresSize = squaressize(CubeCheckerSquares);

global_settings {
ambient_light White * 10
}

camera {
location ObserverPos
look_at (1 - LookAtOrigin) * (ObserverPos + ＜0, 0, -1 * M＞)
right 4/3 * x / ZoomX
up 3/4 * y / ZoomY
}


// Half Earth
intersection {
sphere {
＜0, 0, 0＞, EarthRadius
rotate ＜0, 0, 90＞
rotate ＜-90, 0, 0＞
translate EarthCenter

}

box {
＜-1, -1, -1＞ * EarthRadius * 4,
＜1, 1, 0＞ * EarthRadius * 4
}

texture {
pigment {
checker Gray * 0.5, White
scale ＜EarthCheckerSquaresSize, EarthCheckerSquaresSize, EarthRadius * 4＞
translate ＜0, 0, -EarthRadius * 2＞
}
}
}

// Half cube
box {
＜-1, 0, -1＞ * EarthRadius,
＜1, 2, 0＞ * EarthRadius
texture {
pigment {
checker Blue * 0.5, Yellow
scale ＜CubeCheckerSquaresSize, CubeCheckerSquaresSize, EarthRadius * 4＞
translate ＜0, 0, -EarthRadius * 2＞
}
}
}

// intersection point
sphere {
＜0, 0, 0＞, 1
texture {
pigment {
color rgbf＜1, 0, 0, 1＞
}
}
scale ＜1, 1, 1＞ * ObserverDist / 100
scale ＜1 / ZoomX, 1 / ZoomY, 1＞
}


// reference point
sphere {
＜0, 0, 0＞, 1
texture {
pigment {
color rgbf＜0, 1, 0, 1＞
}
}
scale ＜1, 1, 1＞ * ObserverDist / 100
scale ＜1 / ZoomX, 1 / ZoomY, 1＞
translate ＜RefPointX, - EarthRadius + sqrt(pow(EarthRadius,2) - pow(RefPointX,2)), 0＞
}
//################# POV-Ray model file end ##################