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Checking for a point inside a region of a spherical surface

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Hi everybody, I am working on a 3D Morphing algorithm. I have a point X on lying on a unit sphere in the spherical coordinate system. I have three other points A,B, and C which are also on the unit sphere. The sphere is centered at the origin. I need to find out whether X lies on the spherical 'triangular' area enclosed by A,B, and C or not. Can any one tell me how to do this? Thanks a lot in advance.

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I may not be thinking about this right, but if the point were on the 'triangle', wouldn't it also be on the 'inside' of each of the three planes formed by the sphere center and the triangle vertex pairs?

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I've never actually done this, but the answer seems intuitive enough.

Calculate three planes. Each one is defined by three points: 2 of your "spherical triangle" points and the center of your sphere. Have the normals of the planes pointing "inwards" on your spherical triangle. The space inside those three planes defines your spherical triangle. Check your test point against the planes; if it's on the side of the plane where the normal is pointing, it's inside your spherical triangle.

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