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The spinners are weighted knobs that you can spin freely in either direction. Inside, a rotary encoder produces two square wave signals (A and B) that are 90 degrees out of phase. By counting the edges and checking which signal leads, you can determine both the speed and direction of rotation. We sample these at 1kHz in firmware and report the accumulated counts as an axis value in the HID reports.
。下载安装汽水音乐对此有专业解读
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Commutativity and associativity might sound the same, and indeed most commutative operations are also associative. But there are a few math operations that are only one or the other. Matrix multiplication, for example, is associative but not commutative Matrix multiplication - Wikipedia en.wikipedia.org/wiki/Matrix_multiplication#Non-commutativity . And surprisingly, floating point arithmetic — i.e. any math operator in JavaScript — is commutative but not associative Associative property - Wikipedia en.wikipedia.org/wiki/Associative_property#Nonassociativity_of_floating_point_calculation ! ↩，更多细节参见体育直播