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types:vector [2015-09-22 11:22 SLT] sei style |
types:vector [2015-09-29 08:15 SLT] (current) sei Fix cross product expression |
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| Another type of multiplication is the so called [[http://en.wikipedia.org/wiki/Dot_product|dot product or scalar product]]. It takes two vectors, and the result is a //float//. The symbol is the same as for multiplication of floats and integers, i.e. the asterisk $op[*]. The resulting operation is the sum of the products of the components; for example, if **v** and **w** are vector variables, then ''v * w'' gives the same result as ''v.x * w.x + v.y * w.y + v.z * w.z''. It is useful in several geometric applications. | Another type of multiplication is the so called [[http://en.wikipedia.org/wiki/Dot_product|dot product or scalar product]]. It takes two vectors, and the result is a //float//. The symbol is the same as for multiplication of floats and integers, i.e. the asterisk $op[*]. The resulting operation is the sum of the products of the components; for example, if **v** and **w** are vector variables, then ''v * w'' gives the same result as ''v.x * w.x + v.y * w.y + v.z * w.z''. It is useful in several geometric applications. | ||
| - | A third type of multiplication is called [[http://en.wikipedia.org/wiki/Cross_product|cross product or vector product]]. It takes two vectors, and the result is a //vector//. The symbol is the same as for integer modulo, i.e. the percent sign $op[%]. The operation is a bit complex: if **v** and **w** are vector variables, then ''v % w'' gives the same result as ''<v.y*w.z - v.z*w.y, v.z*w.x - v.x*w.z, v.x*w.z - v.z*w.x>''. This kind of multiplication returns a vector that is perpendicular to both input vectors, and has several uses in geometry applications too. | + | A third type of multiplication is called [[http://en.wikipedia.org/wiki/Cross_product|cross product or vector product]]. It takes two vectors, and the result is a //vector//. The symbol is the same as for integer modulo, i.e. the percent sign $op[%]. The operation is a bit complex: if **v** and **w** are vector variables, then ''v % w'' gives the same result as ''<v.y*w.z - v.z*w.y, v.z*w.x - v.x*w.z, v.x*w.y - v.y*w.x>''. This kind of multiplication returns a vector that is perpendicular to both input vectors, and has several uses in geometry applications too. |
| And finally, there is a fourth type of multiplication: a vector multiplied by a $lty[rotation] returns the vector rotated by the given rotation. For example, if **r** is a rotation that turns 90° counter-clockwise over the positive Z axis, then ''<0, 3, 1> * r'' will result in ''<-3, 0, 1>'', that is, the vector will be rotated over that axis by that angle. | And finally, there is a fourth type of multiplication: a vector multiplied by a $lty[rotation] returns the vector rotated by the given rotation. For example, if **r** is a rotation that turns 90° counter-clockwise over the positive Z axis, then ''<0, 3, 1> * r'' will result in ''<-3, 0, 1>'', that is, the vector will be rotated over that axis by that angle. | ||