diff --git a/src/Magnum/Math/Intersection.h b/src/Magnum/Math/Intersection.h index 16d2f8a1e..ce5eb502b 100644 --- a/src/Magnum/Math/Intersection.h +++ b/src/Magnum/Math/Intersection.h @@ -59,16 +59,16 @@ Returns intersection point positions @f$ t @f$, @f$ u @f$ on both lines: 2D lines are parallel) The two lines intersect if @f$ t @f$ and @f$ u @f$ exist such that: @f[ - \boldsymbol p + t \boldsymbol r = \boldsymbol q + u \boldsymbol s + \boldsymbol{p} + t \boldsymbol{r} = \boldsymbol{q} + u \boldsymbol{s} @f] Crossing both sides with @f$ \boldsymbol{s} @f$, distributing the cross product -and eliminating @f$ \boldsymbol s \times \boldsymbol s = 0 @f$, then solving +and eliminating @f$ \boldsymbol{s} \times \boldsymbol{s} = 0 @f$, then solving for @f$ t @f$ and similarly for @f$ u @f$: @f[ \begin{array}{rcl} - (\boldsymbol p + t \boldsymbol r) \times s & = & (\boldsymbol q + u \boldsymbol s) \times s \\ - t (\boldsymbol r \times s) & = & (\boldsymbol q - \boldsymbol p) \times s \\ - t & = & \cfrac{(\boldsymbol q - \boldsymbol p) \times s}{\boldsymbol r \times \boldsymbol s} \\ - u & = & \cfrac{(\boldsymbol q - \boldsymbol p) \times r}{\boldsymbol r \times \boldsymbol s} + (\boldsymbol{p} + t \boldsymbol{r}) \times \boldsymbol{s} & = & (\boldsymbol{q} + u \boldsymbol{s}) \times \boldsymbol{s} \\ + t (\boldsymbol{r} \times \boldsymbol{s}) & = & (\boldsymbol{q} - \boldsymbol{p}) \times \boldsymbol{s} \\ + t & = & \cfrac{(\boldsymbol{q} - \boldsymbol{p}) \times \boldsymbol{s}}{\boldsymbol{r} \times \boldsymbol{s}} \\ + u & = & \cfrac{(\boldsymbol{q} - \boldsymbol{p}) \times \boldsymbol{r}}{\boldsymbol{r} \times \boldsymbol{s}} \end{array} @f]