The R3 roticvision operation is the inverse of rotication. As seen in an earlier post, rotication requires an amount of rotation, an axis and a starting point in order to calculate the new location of a point.
In contrast, roticvision requires a current point, an axis and an original starting point that are all Opposite Values. The roticvision operation returns an amount of rotation. This is the amount of rotation needed to get from the original starting point to the current point around the given axis using rotication.
Syntax
Roticvision is expressed in R3 as:
(Current Point) /R↺?, (Starting point) = ??o or aπ?.
In roticvision, /R↺ is the Operation, the ? is the axis and together with the original starting point form the Operator. The default is the z-axis, denoted by the pair of Opposite Values (0, 0, 0) and (0, 0, j^). The current point is the Operand. The Operator and Operand must be Opposite Values. Finally, an angle of rotation is the result.
For example, in the equation:
- (14.28^ + 12.7i^ +26.7j^) /R↺(4^ +5i^ + 6j^) (1^ + 2i^ + 3j^) = π^/3
The starting point (1^ + 2i^ + 3j^) and the axis (4^+ 5i^ + 6j) form the operator and the current point (14.28^ + 12.7i^ +26.7j^) represents the Operand. The result is π^/3.
The details of the calculation of roticvision are not yet available. Consequently, the online calculator does not include this operation.
Examples of Roticvision in R3
- (0, iv, 0) /R↺ (1^, 0, 0) = πv/2
- (0, 0, jv) /R↺y (1^, 0, 0) = π^/2
- (0, 8iv, 0) /R↺4v (0, 0, 2jv) = π^/2
- (4.2^ + iv +4.83jv) /R↺(^ + 2i^ + 3j^) (1.061^+1.207iv+ 0.646jv) = π^/4
- π^/4 R↺(^ + 2i^ + 3j^) (1.061^+1.207iv+ 0.646jv)
- = (4.2^ + iv +4.83jv)
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