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Diffstat (limited to 'Master/texmf-dist/source/latex/l3experimental/l3draw/l3draw-points.dtx')
-rw-r--r-- | Master/texmf-dist/source/latex/l3experimental/l3draw/l3draw-points.dtx | 133 |
1 files changed, 132 insertions, 1 deletions
diff --git a/Master/texmf-dist/source/latex/l3experimental/l3draw/l3draw-points.dtx b/Master/texmf-dist/source/latex/l3experimental/l3draw/l3draw-points.dtx index 2e17871c405..82629b50536 100644 --- a/Master/texmf-dist/source/latex/l3experimental/l3draw/l3draw-points.dtx +++ b/Master/texmf-dist/source/latex/l3experimental/l3draw/l3draw-points.dtx @@ -44,7 +44,7 @@ % }^^A % } % -% \date{Released 2021-08-27} +% \date{Released 2021-11-12} % % \maketitle % @@ -477,6 +477,137 @@ % \end{macro} % \end{macro} % +% \begin{macro}[EXP]{\draw_point_intersect_line_circle:nnnnn} +% \begin{macro}[EXP]{\@@_point_intersect_line_circle_auxi:nnnnnnnn} +% \begin{macro}[EXP] +% { +% \@@_point_intersect_line_circle_auxii:nnnnnnnn, +% \@@_point_intersect_line_circle_auxii:fnnnnnnn, +% \@@_point_intersect_line_circle_auxiii:nnnnnnnn, +% \@@_point_intersect_line_circle_auxiii:fffnnnnn +% } +% \begin{macro}[EXP] +% { +% \@@_point_intersect_line_circle_auxiv:nnnnnnnn, +% \@@_point_intersect_line_circle_auxiv:ffnnnnnn +% } +% \begin{macro}[EXP] +% { +% \@@_point_intersect_line_circle_auxv:nnnnn, +% \@@_point_intersect_line_circle_auxv:fnnnn +% } +% The intersection points~$P_{1}$ and~$P_{2}$ between +% a line joining points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ +% and a circle with center $(x_{3}, y_{3})$ and radius~$r$. +% We use the intermediate +% values +% \begin{align*} +% a &= (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} \\ +% b &= 2 \times ((x_{2} - x_{1}) \times (x_{1} - x_{3}) + (y_{2} - y_{1}) \times (y_{1} - y_{3})) \\ +% c &= x_{3}^{2} + y_{3}^{2} + x_{1}^{2} + y_{1}^{2} +% - 2\times(x_{3} \times x_{1} + y_{3} \times y_{1}) - r^{2} \\ +% d &= b^{2} - 4\times a \times c \\ +% \mu_{1} &= \frac{-b + \sqrt{d}}{2 \times a}\\ +% \mu_{2} &= \frac{-b - \sqrt{d}}{2 \times a} +% \end{align*} +% in either +% \begin{align*} +% P_{1x} &= x_{1} + \mu_{1}\times (x_{2} - x_{1}) \\ +% P_{1y} &= y_{1} + \mu_{1}\times (y_{2} - y_{1}) +% \end{align*} +% or +% \begin{align*} +% P_{2x} &= x_{1} + \mu_{2}\times (x_{2} - x_{1}) \\ +% P_{2y} &= y_{1} + \mu_{2}\times (y_{2} - y_{1}) +% \end{align*} +% depending on which solution is required. The rest of the work is simply +% forcing the appropriate expansion and shuffling arguments. +% \begin{macrocode} +\cs_new:Npn \draw_point_intersect_line_circle:nnnnn #1#2#3#4#5 + { + \@@_point_process:nnnn + { \@@_point_intersect_line_circle_auxi:nnnnnnnn {#4} {#5} } + {#1} {#2} {#3} + } +\cs_new:Npn \@@_point_intersect_line_circle_auxi:nnnnnnnn #1#2#3#4#5#6#7#8 + { + \@@_point_intersect_line_circle_auxii:fnnnnnnn + { \fp_eval:n {#1} } {#3} {#4} {#5} {#6} {#7} {#8} {#2} + } +% \end{macrocode} +% At this stage we have all of the information we need, fully expanded: +% \begin{enumerate}[label = \#\arabic*, font = \ttfamily] +% \item $r$ +% \item $x_{1}$ +% \item $y_{1}$ +% \item $x_{2}$ +% \item $y_{2}$ +% \item $x_{3}$ +% \item $y_{3}$ +% \item $n$ +% \end{enumerate} +% Once we evaluate $a$, $b$ and $c$, the co-ordinate $(x_{3},y_{3})$ +% and $r$ are no longer required: handy as we will need various +% intermediate values in the following. +% \begin{macrocode} +\cs_new:Npn \@@_point_intersect_line_circle_auxii:nnnnnnnn #1#2#3#4#5#6#7#8 + { + \@@_point_intersect_line_circle_auxiii:fffnnnnn + { \fp_eval:n { (#4-#2)*(#4-#2)+(#5-#3)*(#5-#3) } } + { \fp_eval:n { 2*((#4-#2)*(#2-#6)+(#5-#3)*(#3-#7)) } } + { \fp_eval:n { (#6*#6+#7*#7)+(#2*#2+#3*#3)-(2*(#6*#2+#7*#3))-(#1*#1) } } + {#2} {#3} {#4} {#5} {#8} + } +\cs_generate_variant:Nn \@@_point_intersect_line_circle_auxii:nnnnnnnn { f } +% \end{macrocode} +% then we can get $d = b^{2} - 4\times a \times c$ and the usage of $n$. +% \begin{macrocode} +\cs_new:Npn \@@_point_intersect_line_circle_auxiii:nnnnnnnn #1#2#3#4#5#6#7#8 + { + \@@_point_intersect_line_circle_auxiv:ffnnnnnn + { \fp_eval:n { #2 * #2 - 4 * #1 * #3 } } + { \int_if_odd:nTF {#8} { 1 } { -1 } } + {#1} {#2} {#4} {#5} {#6} {#7} + } +\cs_generate_variant:Nn \@@_point_intersect_line_circle_auxiii:nnnnnnnn { fff } +% \end{macrocode} +% We now have all of the intermediate values we require, with one division +% carried out up-front to avoid doing this expensive step twice: +% \begin{enumerate}[label = \#\arabic*, font = \ttfamily] +% \item $a$ +% \item $b$ +% \item $c$ +% \item $d$ +% \item $\pm$(the usage of $n$) +% \item $x_{1}$ +% \item $y_{1}$ +% \item $x_{2}$ +% \item $y_{2}$ +% \end{enumerate} +% There are some final pre-calculations, +% $\mu = \frac{-b \pm \sqrt{d}}{2 \times a}$ +% then, we can yield a result. +% \begin{macrocode} +\cs_new:Npn \@@_point_intersect_line_circle_auxiv:nnnnnnnn #1#2#3#4#5#6#7#8 + { + \@@_point_intersect_line_circle_auxv:fnnnn + { \fp_eval:n { (-1 * #4 + #2 * sqrt(#1)) / (2 * #3) } } + {#5} {#6} {#7} {#8} + } +\cs_generate_variant:Nn \@@_point_intersect_line_circle_auxiv:nnnnnnnn { ff } +\cs_new:Npn \@@_point_intersect_line_circle_auxv:nnnnn #1#2#3#4#5 + { + \draw_point:n + { #2 + #1 * (#4 - #2), #3 + #1 * (#5 - #3) } + } +\cs_generate_variant:Nn \@@_point_intersect_line_circle_auxv:nnnnn { f } +% \end{macrocode} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% \end{macro} +% % \subsection{Interpolation on a line (vector) or arc} % % \begin{macro}[EXP]{\draw_point_interpolate_line:nnn} |