summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/tex/latex/hobby/hobby.code.tex
diff options
context:
space:
mode:
authorKarl Berry <karl@freefriends.org>2012-09-03 22:56:48 +0000
committerKarl Berry <karl@freefriends.org>2012-09-03 22:56:48 +0000
commit49ee169240901a3f97d82ab2e35e37cf237b3961 (patch)
tree75a8e3f59aebd5cac9c9132f0bdbd606052cde67 /Master/texmf-dist/tex/latex/hobby/hobby.code.tex
parent8028e80de243e75b6cd0bdc9aec5dbed7c6be192 (diff)
new tikz package hobby (3sep12)
git-svn-id: svn://tug.org/texlive/trunk@27584 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/tex/latex/hobby/hobby.code.tex')
-rw-r--r--Master/texmf-dist/tex/latex/hobby/hobby.code.tex640
1 files changed, 640 insertions, 0 deletions
diff --git a/Master/texmf-dist/tex/latex/hobby/hobby.code.tex b/Master/texmf-dist/tex/latex/hobby/hobby.code.tex
new file mode 100644
index 00000000000..70555c1973c
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/hobby/hobby.code.tex
@@ -0,0 +1,640 @@
+%%
+%% This is file `hobby.code.tex',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% hobby.dtx (with options: `hobby')
+%% ----------------------------------------------------------------
+%% hobby --- a TikZ/PGF library for drawing smooth(ish) curves using
+%% Hobby's algorithm (implemented in LaTeX3)
+%% E-mail: stacey@math.ntnu.no
+%% Released under the LaTeX Project Public License v1.3c or later
+%% See http://www.latex-project.org/lppl.txt
+%% ----------------------------------------------------------------
+%%
+\RequirePackage{expl3}
+\RequirePackage{xparse}
+\RequirePackage{pml3array}
+\ExplSyntaxOn
+\cs_generate_variant:Nn \fp_set:Nn {Nx}
+\fp_new:N \g_hobby_parama_fp
+\fp_new:N \g_hobby_paramb_fp
+\fp_new:N \g_hobby_paramc_fp
+
+\fp_gset:Nn \g_hobby_parama_fp {2^.5}
+
+\fp_gset:Nn \g_hobby_paramb_fp {1/16}
+
+\fp_gset:Nn \g_hobby_paramc_fp {(3-5^.5)/2}
+\bool_new:N \l_hobby_closed_bool
+\bool_new:N \l_hobby_disjoint_bool
+\array_new:N \l_hobby_points_array
+\array_new:N \l_hobby_points_x_array
+\array_new:N \l_hobby_points_y_array
+\array_new:N \l_hobby_angles_array
+\array_new:N \l_hobby_distances_array
+\array_new:N \l_hobby_tension_out_array
+\array_new:N \l_hobby_tension_in_array
+\array_new:N \l_hobby_matrix_a_array
+\array_new:N \l_hobby_matrix_b_array
+\array_new:N \l_hobby_matrix_c_array
+\array_new:N \l_hobby_matrix_d_array
+\array_new:N \l_hobby_vector_u_array
+\array_new:N \l_hobby_excess_angle_array
+\array_new:N \l_hobby_psi_array
+\array_new:N \l_hobby_theta_array
+\array_new:N \l_hobby_phi_array
+\array_new:N \l_hobby_sigma_array
+\array_new:N \l_hobby_rho_array
+\array_new:N \l_hobby_controla_array
+\array_new:N \l_hobby_controlb_array
+\fp_new:N \l_hobby_matrix_v_fp
+\fp_new:N \l_hobby_tempa_fp
+\fp_new:N \l_hobby_tempb_fp
+\fp_new:N \l_hobby_tempc_fp
+\fp_new:N \l_hobby_tempd_fp
+\fp_new:N \l_hobby_temps_fp
+\fp_new:N \l_hobby_in_curl_fp
+\fp_set:Nn \l_hobby_in_curl_fp {1}
+\fp_new:N \l_hobby_out_curl_fp
+\fp_set:Nn \l_hobby_out_curl_fp {1}
+\fp_new:N \l_hobby_in_angle_fp
+\fp_set_eq:NN \l_hobby_in_angle_fp \c_undefined_fp
+\fp_new:N \l_hobby_out_angle_fp
+\fp_set_eq:NN \l_hobby_out_angle_fp \c_undefined_fp
+\int_new:N \l_hobby_npoints_int
+\keys_define:nn {hobby / read in all} {
+ x .fp_set:N = \l_hobby_tempa_fp,
+ y .fp_set:N = \l_hobby_tempb_fp,
+ tension~out .fp_set:N = \l_hobby_tempc_fp,
+ tension~in .fp_set:N = \l_hobby_tempd_fp,
+ excess~angle .fp_set:N = \l_hobby_temps_fp,
+ tension .meta:n = { tension~out=#1, tension~in=#1 },
+ tension~out .default:n = 1,
+ tension~in .default:n = 1,
+ excess~angle .default:n = 0,
+ in~angle .fp_set:N = \l_hobby_in_angle_fp,
+ out~angle .fp_set:N = \l_hobby_out_angle_fp,
+ in~curl .fp_set:N = \l_hobby_in_curl_fp,
+ out~curl .fp_set:N = \l_hobby_out_curl_fp,
+ closed .bool_set:N = \l_hobby_closed_bool,
+ closed .default:n = true,
+ disjoint .bool_set:N = \l_hobby_disjoint_bool,
+ disjoint .default:n = true,
+}
+\keys_define:nn { hobby / read in params} {
+ in~angle .fp_set:N = \l_hobby_in_angle_fp,
+ out~angle .fp_set:N = \l_hobby_out_angle_fp,
+ in~curl .fp_set:N = \l_hobby_in_curl_fp,
+ out~curl .fp_set:N = \l_hobby_out_curl_fp,
+ closed .bool_set:N = \l_hobby_closed_bool,
+ closed .default:n = true,
+ disjoint .bool_set:N = \l_hobby_disjoint_bool,
+ disjoint .default:n = true,
+}
+\cs_set:Nn \hobby_distangle:n {
+ \fp_set:Nn \l_hobby_tempa_fp {
+ (\array_get:Nn \l_hobby_points_x_array {#1 + 1})
+ - (\array_get:Nn \l_hobby_points_x_array {#1})}
+
+ \fp_set:Nn \l_hobby_tempb_fp {
+ (\array_get:Nn \l_hobby_points_y_array {#1 + 1})
+ - (\array_get:Nn \l_hobby_points_y_array {#1})}
+
+ \fp_atantwo:NNN \l_hobby_tempc_fp \l_hobby_tempb_fp \l_hobby_tempa_fp
+ \fp_veclen:NVV \l_hobby_tempd_fp \l_hobby_tempa_fp \l_hobby_tempb_fp
+
+ \array_push:Nx \l_hobby_angles_array {\fp_to_tl:N \l_hobby_tempc_fp}
+ \array_push:Nx \l_hobby_distances_array {\fp_to_tl:N \l_hobby_tempd_fp}
+ }
+\cs_new:Nn \fp_atantwo:NNN {
+ \pgfmathparse{rad(atan2(\fp_use:N #3,\fp_use:N #2))}
+ \exp_args:NNo \fp_set:Nn #1 {\pgfmathresult}
+}
+\cs_new:Nn \fp_veclen:Nnn {
+ \fp_set:Nn #1 {((#2)^2 + (#3)^2)^.5}
+}
+\cs_generate_variant:Nn \fp_veclen:Nnn {NVV}
+\cs_new:Nn \hobby_ctrllen:Nnn {
+ \fp_set:Nn #1 {(2 - \g_hobby_parama_fp
+ * ( sin(#2) - \g_hobby_paramb_fp * sin(#3) )
+ * ( sin(#3) - \g_hobby_paramb_fp * sin(#2) )
+ * ( cos(#2) - cos(#3) ) )
+ / ( 1 + (1 - \g_hobby_paramc_fp) * cos(#3) + \g_hobby_paramc_fp * cos(#2))}
+}
+\cs_generate_variant:Nn \hobby_ctrllen:Nnn {NVV}
+\cs_new_protected:Npn \hobby_append_point_copy:n #1
+ {
+ \hobby_append_point_copy_aux:Nn \l_hobby_points_array {#1}
+ \hobby_append_point_copy_aux:Nn \l_hobby_points_x_array {#1}
+ \hobby_append_point_copy_aux:Nn \l_hobby_points_y_array {#1}
+ \hobby_append_point_copy_aux:Nn \l_hobby_tension_in_array {#1}
+ \hobby_append_point_copy_aux:Nn \l_hobby_tension_out_array {#1}
+ \hobby_append_point_copy_aux:Nn \l_hobby_excess_angle_array {#1}
+ }
+\cs_new_protected:Npn \hobby_append_point_copy_aux:Nn #1#2
+ { \array_push:Nx #1 { \array_get:Nn #1 {#2} } }
+\cs_new:Nn \hobby_genpath:
+{
+\bool_if:NT \l_hobby_closed_bool {
+ \fp_compare:nTF {(\array_get:Nn \l_hobby_points_x_array {0})
+ =
+ (\array_top:N \l_hobby_points_x_array)}
+ {
+ \fp_compare:nF {
+ \array_get:Nn \l_hobby_points_y_array {0}
+ =
+ \array_top:N \l_hobby_points_y_array
+ }
+ {
+ \hobby_append_point_copy:n {0}
+ }
+ }
+ {
+ \hobby_append_point_copy:n {0}
+ }
+ \hobby_append_point_copy:n {1}
+}
+\int_set:Nn \l_hobby_npoints_int {\array_length:N \l_hobby_points_y_array}
+
+\prg_stepwise_function:nnnN {0} {1} {\l_hobby_npoints_int - 1} \hobby_distangle:n
+ \prg_stepwise_inline:nnnn {1} {1} {\l_hobby_npoints_int - 1} {
+ \fp_set:Nx \l_hobby_tempa_fp {
+ \array_get:Nn \l_hobby_angles_array {##1}
+ - \array_get:Nn \l_hobby_angles_array {##1 - 1}}
+ \fp_compare:nTF {\l_hobby_tempa_fp > \c_pi_fp }
+ {
+ \fp_sub:Nn \l_hobby_tempa_fp {2 * \c_pi_fp}
+ }
+ {}
+ \fp_compare:nTF {\l_hobby_tempa_fp < -\c_pi_fp }
+ {
+ \fp_add:Nn \l_hobby_tempa_fp {2 * \c_pi_fp}
+ }
+ {}
+\array_get:NnNTF \l_hobby_excess_angle_array {##1} \l_tmpa_tl {
+ \fp_add:Nn \l_hobby_tempa_fp {2 * \c_pi_fp * \l_tmpa_tl}
+ }{}
+ \array_put:Nnx \l_hobby_psi_array {##1}{\fp_to_tl:N \l_hobby_tempa_fp}
+ }
+ \prg_stepwise_inline:nnnn {1} {1} {\l_hobby_npoints_int - 1} {
+ \array_put:Nnx \l_hobby_matrix_a_array {##1} {\fp_to_tl:n {
+ \array_get:Nn \l_hobby_tension_in_array {##1}^2
+ * \array_get:Nn \l_hobby_distances_array {##1}
+ * \array_get:Nn \l_hobby_tension_in_array {##1 + 1}
+ }}
+}
+ \prg_stepwise_inline:nnnn {1} {1} {\l_hobby_npoints_int - 1} {
+
+ \array_put:Nnx \l_hobby_matrix_b_array {##1} {\fp_to_tl:n
+{(3 * (\array_get:Nn \l_hobby_tension_in_array {##1 + 1}) - 1) *
+ (\array_get:Nn \l_hobby_tension_out_array {##1})^2 *
+(\array_get:Nn \l_hobby_tension_out_array {##1 - 1})
+* ( \array_get:Nn \l_hobby_distances_array {##1 - 1})
++
+(3 * (\array_get:Nn \l_hobby_tension_out_array {##1 - 1}) - 1)
+* (\array_get:Nn \l_hobby_tension_in_array {##1})^2
+* (\array_get:Nn \l_hobby_tension_in_array {##1 + 1})
+* (\array_get:Nn \l_hobby_distances_array {##1})}
+}
+}
+ \prg_stepwise_inline:nnnn {1} {1} {\l_hobby_npoints_int - 2} {
+
+ \array_put:Nnx \l_hobby_matrix_c_array {##1} {\fp_to_tl:n
+{(\array_get:Nn \l_hobby_tension_in_array {##1})^2
+* (\array_get:Nn \l_hobby_tension_in_array {##1 - 1})
+* (\array_get:Nn \l_hobby_distances_array {##1 - 1})
+}}
+
+}
+ \prg_stepwise_inline:nnnn {1} {1} {\l_hobby_npoints_int - 2} {
+
+ \array_put:Nnx \l_hobby_matrix_d_array {##1} {\fp_to_tl:n
+{
+- (\array_get:Nn \l_hobby_psi_array {##1 + 1})
+* (\array_get:Nn \l_hobby_tension_out_array {##1})^2
+* (\array_get:Nn \l_hobby_tension_out_array {##1 - 1})
+* (\array_get:Nn \l_hobby_distances_array {##1 - 1})
+- (3 * (\array_get:Nn \l_hobby_tension_out_array {##1 - 1}) - 1)
+* (\array_get:Nn \l_hobby_psi_array {##1})
+* (\array_get:Nn \l_hobby_tension_in_array {##1})^2
+* (\array_get:Nn \l_hobby_tension_in_array {##1 + 1})
+* (\array_get:Nn \l_hobby_distances_array {##1})
+}
+}
+}
+\bool_if:NTF \l_hobby_closed_bool {
+\array_put:Nnx \l_hobby_matrix_c_array {0} {\fp_to_tl:n {
+- (\array_get:Nn \l_hobby_distances_array {\l_hobby_npoints_int - 2})
+* (\array_get:Nn \l_hobby_tension_out_array {\l_hobby_npoints_int - 2})
+* (\array_get:Nn \l_hobby_tension_out_array {\l_hobby_npoints_int - 1})^2
+}}
+
+\array_put:Nnn \l_hobby_matrix_b_array {0} {1}
+\array_put:Nnn \l_hobby_matrix_d_array {0} {0}
+
+\array_put:Nnx \l_hobby_matrix_b_array {\l_hobby_npoints_int - 1} {\fp_to_tl:n {
+(\array_get:Nn \l_hobby_matrix_b_array {\l_hobby_npoints_int - 1})
++ 1
+}}
+
+ \array_put:Nnx \l_hobby_matrix_d_array {\l_hobby_npoints_int - 1} {\fp_to_tl:n {
+- (\array_get:Nn \l_hobby_psi_array {1})
+* (\array_get:Nn \l_hobby_tension_out_array {\l_hobby_npoints_int -1})^2
+* (\array_get:Nn \l_hobby_tension_out_array {\l_hobby_npoints_int -2})
+* (\array_get:Nn \l_hobby_distances_array {\l_hobby_npoints_int - 2})
+- (3 * (\array_get:Nn \l_hobby_tension_out_array {\l_hobby_npoints_int - 2}) - 1)
+* (\array_get:Nn \l_hobby_psi_array {\l_hobby_npoints_int - 1})
+* (\array_get:Nn \l_hobby_tension_in_array {\l_hobby_npoints_int - 1})^2
+* (\array_get:Nn \l_hobby_tension_in_array {\l_hobby_npoints_int})
+* (\array_get:Nn \l_hobby_distances_array {\l_hobby_npoints_int -1})
+}
+}
+ \array_put:Nnn \l_hobby_vector_u_array {0} {1}
+\array_put:Nnn \l_hobby_vector_u_array {\l_hobby_npoints_int - 1} {1}
+ \prg_stepwise_inline:nnnn {1} {1} {\l_hobby_npoints_int - 2} {
+ \array_put:Nnn \l_hobby_vector_u_array {##1} {0}
+ }
+\fp_set:Nn \l_hobby_matrix_v_fp {
+(\array_get:Nn \l_hobby_tension_out_array {\l_hobby_npoints_int -1})^2
+* (\array_get:Nn \l_hobby_tension_out_array {\l_hobby_npoints_int -2})
+* (\array_get:Nn \l_hobby_distances_array {\l_hobby_npoints_int -2})
+}
+}
+{
+\fp_if_undefined:NTF \l_hobby_out_angle_fp
+{
+ \array_put:Nnx \l_hobby_matrix_b_array {0} {\fp_to_tl:n {
+ (\array_get:Nn \l_hobby_tension_in_array {1})^3
+* \l_hobby_in_curl_fp
++
+(3 * (\array_get:Nn \l_hobby_tension_in_array {1}) - 1)
+* (\array_get:Nn \l_hobby_tension_out_array {0})^3
+}}
+
+ \array_put:Nnx \l_hobby_matrix_c_array {0} {\fp_to_tl:n {
+ (\array_get:Nn \l_hobby_tension_out_array {0})^3
++
+(3 * (\array_get:Nn \l_hobby_tension_out_array {0}) - 1)
+* (\array_get:Nn \l_hobby_tension_in_array {1})^3
+* \l_hobby_in_curl_fp
+}}
+
+ \array_put:Nnx \l_hobby_matrix_d_array {0} {\fp_to_tl:n {
+-( (\array_get:Nn \l_hobby_tension_out_array {0})^3
++
+(3 * (\array_get:Nn \l_hobby_tension_out_array {0}) - 1)
+* (\array_get:Nn \l_hobby_tension_in_array {1})^3
+* \l_hobby_in_curl_fp)
+* (\array_get:Nn \l_hobby_psi_array {1})
+}}
+
+}
+{
+ \array_put:Nnn \l_hobby_matrix_b_array {0} {1}
+ \array_put:Nnn \l_hobby_matrix_c_array {0} {0}
+ \fp_set:Nn \l_hobby_tempa_fp { \l_hobby_out_angle_fp
+ - \array_get:Nn \l_hobby_angles_array {0} }
+ \fp_compare:nT {\l_hobby_tempa_fp > \c_pi_fp }
+ {
+ \fp_sub:Nn \l_hobby_tempa_fp {2 * \c_pi_fp}
+ }
+ \fp_compare:nT {\l_hobby_tempa_fp < -\c_pi_fp }
+ {
+ \fp_add:Nn \l_hobby_tempa_fp {2 * \c_pi_fp}
+ }
+ \array_put:Nnx \l_hobby_matrix_d_array {0} {\fp_to_tl:N \l_hobby_tempa_fp}
+}
+\fp_if_undefined:NTF \l_hobby_in_angle_fp
+{
+
+ \array_put:Nnx \l_hobby_matrix_b_array {\l_hobby_npoints_int - 1} {\fp_to_tl:n {
+\array_get:Nn \l_hobby_matrix_b_array {\l_hobby_npoints_int - 1}
+- (\array_get:Nn \l_hobby_tension_out_array {\l_hobby_npoints_int - 1})^2
+* (\array_get:Nn \l_hobby_tension_out_array {\l_hobby_npoints_int - 2})
+* (\array_get:Nn \l_hobby_distances_array {\l_hobby_npoints_int - 2})
+*
+((3 * (\array_get:Nn \l_hobby_tension_in_array {\l_hobby_npoints_int} ) - 1)
+* (\array_get:Nn \l_hobby_tension_out_array {\l_hobby_npoints_int - 1})^3 \l_tmpa_tl
+* \l_hobby_out_curl_fp
++
+(\array_get:Nn \l_hobby_tension_in_array {\l_hobby_npoints_int })^3)
+/
+((3 * (\array_get:Nn \l_hobby_tension_out_array {\l_hobby_npoints_int -2}) - 1)
+* (\array_get:Nn \l_hobby_tension_in_array {\l_hobby_npoints_int})^3
++
+( \array_get:Nn \l_hobby_tension_out_array {\l_hobby_npoints_int - 1})^3
+* \l_hobby_out_curl_fp)
+}}
+
+ \array_put:Nnx \l_hobby_matrix_d_array {\l_hobby_npoints_int - 1} {\fp_to_tl:n {
+- (3 * (\array_get:Nn \l_hobby_tension_out_array {\l_hobby_npoints_int - 2}) - 1)
+* (\array_get:Nn \l_hobby_psi_array {\l_hobby_npoints_int - 1})
+* (\array_get:Nn \l_hobby_tension_in_array {\l_hobby_npoints_int - 1})^2
+* (\array_get:Nn \l_hobby_tension_in_array {\l_hobby_npoints_int})
+* (\array_get:Nn \l_hobby_distances_array {\l_hobby_npoints_int - 1})
+}}
+
+}
+{
+ \fp_set:Nn \l_hobby_tempa_fp { - \l_hobby_in_angle_fp + \c_pi_fp
++ (\array_get:Nn \l_hobby_angles_array {\l_hobby_npoints_int - 1})}
+ \fp_compare:nT {\l_hobby_tempa_fp > \c_pi_fp }
+ {
+ \fp_sub:Nn \l_hobby_tempa_fp {2 * \c_pi_fp}
+ }
+ \fp_compare:nT {\l_hobby_tempa_fp < -\c_pi_fp }
+ {
+ \fp_add:Nn \l_hobby_tempa_fp {2 * \c_pi_fp}
+ }
+
+ \array_put:Nnx \l_hobby_phi_array {\l_hobby_npoints_int}
+ {\fp_to_tl:N \l_hobby_tempa_fp}
+
+ \array_put:Nnx \l_hobby_matrix_d_array {\l_hobby_npoints_int - 1} {\fp_to_tl:n {
+ \l_hobby_tempa_fp
+ * (\array_get:Nn \l_hobby_tension_out_array {\l_hobby_npoints_int - 1})^2
+* (\array_get:Nn \l_hobby_tension_out_array {\l_hobby_npoints_int - 2})
+* (\array_get:Nn \l_hobby_distances_array {\l_hobby_npoints_int - 2})
+-
+(3 * ( \array_get:Nn \l_hobby_tension_out_array {\l_hobby_npoints_int - 2}) - 1)
+* (\array_get:Nn \l_hobby_psi_array {\l_hobby_npoints_int - 1})
+* (\array_get:Nn \l_hobby_tension_in_array {\l_hobby_npoints_int - 1})^2
+* (\array_get:Nn \l_hobby_tension_in_array {\l_hobby_npoints_int})
+* (\array_get:Nn \l_hobby_distances_array {\l_hobby_npoints_int - 1}) }}
+}
+}
+\prg_stepwise_inline:nnnn {1} {1} {\l_hobby_npoints_int - 1} {
+
+ \array_put:Nnx \l_hobby_matrix_b_array {##1} {\fp_to_tl:n {
+ (\array_get:Nn \l_hobby_matrix_b_array {##1 - 1})
+* (\array_get:Nn \l_hobby_matrix_b_array {##1})
+-
+(\array_get:Nn \l_hobby_matrix_c_array {##1 - 1})
+* (\array_get:Nn \l_hobby_matrix_a_array {##1})
+}}
+ \int_compare:nT {##1 < \l_hobby_npoints_int - 1} {
+
+ \array_put:Nnx \l_hobby_matrix_c_array {##1} {\fp_to_tl:n {
+(\array_get:Nn \l_hobby_matrix_b_array {##1 - 1})
+ * (\array_get:Nn \l_hobby_matrix_c_array {##1})
+}}
+ }
+
+ \array_put:Nnx \l_hobby_matrix_d_array {##1} {\fp_to_tl:n {
+(\array_get:Nn \l_hobby_matrix_b_array {##1 - 1})
+ * (\array_get:Nn \l_hobby_matrix_d_array {##1})
+-
+ (\array_get:Nn \l_hobby_matrix_d_array {##1 - 1})
+ * (\array_get:Nn \l_hobby_matrix_a_array {##1})
+}}
+ \bool_if:NT \l_hobby_closed_bool {
+ \array_put:Nnx \l_hobby_vector_u_array {##1} {\fp_to_tl:n {
+(\array_get:Nn \l_hobby_matrix_b_array {##1 - 1})
+* (\array_get:Nn \l_hobby_vector_u_array {##1})
+-
+(\array_get:Nn \l_hobby_vector_u_array {##1 - 1})
+* (\array_get:Nn \l_hobby_matrix_a_array {##1})
+}}
+}
+}
+ \array_put:Nnx \l_hobby_theta_array {\l_hobby_npoints_int - 1} {\fp_to_tl:n {
+(\array_get:Nn \l_hobby_matrix_d_array {\l_hobby_npoints_int - 1})
+/ (\array_get:Nn \l_hobby_matrix_b_array {\l_hobby_npoints_int - 1})
+}}
+\bool_if:NT \l_hobby_closed_bool {
+ \array_put:Nnx \l_hobby_vector_u_array {\l_hobby_npoints_int - 1} {\fp_to_tl:n {
+ (\array_get:Nn \l_hobby_vector_u_array {\l_hobby_npoints_int - 1})
+/ (\array_get:Nn \l_hobby_matrix_b_array {\l_hobby_npoints_int - 1})
+}}
+}
+\prg_stepwise_inline:nnnn {\l_hobby_npoints_int - 2} {-1} {0} {
+
+ \array_put:Nnx \l_hobby_theta_array {##1} {\fp_to_tl:n {
+( (\array_get:Nn \l_hobby_matrix_d_array {##1})
+ - (\array_get:Nn \l_hobby_theta_array {##1 + 1})
+ * (\array_get:Nn \l_hobby_matrix_c_array {##1})
+) / (\array_get:Nn \l_hobby_matrix_b_array {##1})
+}}
+}
+\bool_if:NT \l_hobby_closed_bool {
+\prg_stepwise_inline:nnnn {\l_hobby_npoints_int - 2} {-1} {0} {
+ \array_put:Nnx \l_hobby_vector_u_array {##1} {\fp_to_tl:n
+{
+ ((\array_get:Nn \l_hobby_vector_u_array {##1})
+ - (\array_get:Nn \l_hobby_vector_u_array {##1 + 1})
+ * (\array_get:Nn \l_hobby_matrix_c_array {##1})
+ ) / (\array_get:Nn \l_hobby_matrix_b_array {##1})
+}}
+}
+
+\fp_set:Nn \l_hobby_tempb_fp {
+((\array_get:Nn \l_hobby_theta_array {1})
+* \l_hobby_matrix_v_fp
+- (\array_get:Nn \l_hobby_theta_array {\l_hobby_npoints_int - 1})
+) / (
+(\array_get:Nn \l_hobby_vector_u_array {1})
+* \l_hobby_matrix_v_fp
+- (\array_get:Nn \l_hobby_vector_u_array {\l_hobby_npoints_int - 1})
++ 1
+)}
+
+\prg_stepwise_inline:nnnn {0} {1} {\l_hobby_npoints_int - 1} {
+
+ \array_put:Nnx \l_hobby_theta_array {##1} {\fp_to_tl:n {
+ (\array_get:Nn \l_hobby_theta_array {##1})
+ - (\array_get:Nn \l_hobby_vector_u_array {##1})
+ * \l_hobby_tempb_fp
+}}
+}
+}
+\prg_stepwise_inline:nnnn {1} {1} {\l_hobby_npoints_int - 1} {
+
+ \array_put:Nnx \l_hobby_phi_array {##1} {\fp_to_tl:n {
+ - (\array_get:Nn \l_hobby_psi_array {##1})
+ - (\array_get:Nn \l_hobby_theta_array {##1})
+ }}
+ }
+\bool_if:NTF \l_hobby_closed_bool {
+ \int_decr:N \l_hobby_npoints_int
+}{
+\fp_if_undefined:NT \l_hobby_in_angle_fp
+{
+ \array_put:Nnx \l_hobby_phi_array {\l_hobby_npoints_int} {\fp_to_tl:n {
+((3 * (\array_get:Nn \l_hobby_tension_in_array {\l_hobby_npoints_int}) - 1)
+* (\array_get:Nn \l_hobby_tension_out_array {\l_hobby_npoints_int - 1})^3
+* \l_hobby_out_curl_fp
++
+(\array_get:Nn \l_hobby_tension_in_array {\l_hobby_npoints_int })^3)
+/
+((3 * (\array_get:Nn \l_hobby_tension_out_array {\l_hobby_npoints_int -2}) - 1)
+* (\array_get:Nn \l_hobby_tension_in_array {\l_hobby_npoints_int})^3 \l_tmpa_tl
++
+(\array_get:Nn \l_hobby_tension_out_array {\l_hobby_npoints_int - 1})^3
+* \l_hobby_out_curl_fp)
+*
+(\array_get:Nn \l_hobby_theta_array {\l_hobby_npoints_int -1})
+}}
+}
+}
+\prg_stepwise_inline:nnnn {0} {1} {\l_hobby_npoints_int - 1} {
+
+ \fp_set:Nn \l_hobby_tempa_fp {\array_get:Nn \l_hobby_theta_array {##1}}
+
+ \fp_set:Nn \l_hobby_tempb_fp {\array_get:Nn \l_hobby_phi_array {##1 + 1}}
+
+ \hobby_ctrllen:NVV \l_hobby_temps_fp \l_hobby_tempa_fp \l_hobby_tempb_fp
+
+ \array_put:Nnx \l_hobby_sigma_array {##1 + 1} {\fp_to_tl:N \l_hobby_temps_fp}
+
+ \hobby_ctrllen:NVV \l_hobby_temps_fp \l_hobby_tempb_fp \l_hobby_tempa_fp
+
+ \array_put:Nnx \l_hobby_rho_array {##1} {\fp_to_tl:N \l_hobby_temps_fp}
+
+ }
+\prg_stepwise_inline:nnnn {0} {1} {\l_hobby_npoints_int - 1} {
+
+\array_put:Nnx \l_hobby_controla_array {##1 + 1} {x = \fp_eval:n {
+(\array_get:Nn \l_hobby_points_x_array {##1})
++
+ (\array_get:Nn \l_hobby_distances_array {##1}) *
+ (\array_get:Nn \l_hobby_rho_array {##1}) *
+cos ( (\array_get:Nn \l_hobby_angles_array {##1})
++
+ (\array_get:Nn \l_hobby_theta_array {##1}))
+/3
+}, y = \fp_eval:n {
+( \array_get:Nn \l_hobby_points_y_array {##1}) +
+ (\array_get:Nn \l_hobby_distances_array {##1}) *
+ (\array_get:Nn \l_hobby_rho_array {##1}) *
+sin ( (\array_get:Nn \l_hobby_angles_array {##1})
++
+ (\array_get:Nn \l_hobby_theta_array {##1}))
+/3
+}
+}
+}
+
+\prg_stepwise_inline:nnnn {1} {1} {\l_hobby_npoints_int} {
+ \array_put:Nnx \l_hobby_controlb_array {##1} {
+ x = \fp_eval:n {\array_get:Nn \l_hobby_points_x_array {##1}
+- (\array_get:Nn \l_hobby_distances_array {##1 - 1})
+* (\array_get:Nn \l_hobby_sigma_array {##1})
+* cos((\array_get:Nn \l_hobby_angles_array {##1 - 1})
+- (\array_get:Nn \l_hobby_phi_array {##1}))/3
+}, y = \fp_eval:n {
+ (\array_get:Nn \l_hobby_points_y_array {##1})
+- (\array_get:Nn \l_hobby_distances_array {##1 - 1})
+* (\array_get:Nn \l_hobby_sigma_array {##1})
+* sin((\array_get:Nn \l_hobby_angles_array {##1 - 1})
+- (\array_get:Nn \l_hobby_phi_array {##1}))/3
+} }
+ }
+}
+\NewDocumentCommand \hobbyinit {m m m} {
+\hobby_set_cmds:nnn#1#2#3
+\array_clear:N \l_hobby_points_array
+\array_clear:N \l_hobby_points_x_array
+\array_clear:N \l_hobby_points_y_array
+\array_clear:N \l_hobby_angles_array
+\array_clear:N \l_hobby_distances_array
+\array_clear:N \l_hobby_tension_out_array
+\array_clear:N \l_hobby_tension_in_array
+\array_clear:N \l_hobby_excess_angle_array
+\array_clear:N \l_hobby_matrix_a_array
+\array_clear:N \l_hobby_matrix_b_array
+\array_clear:N \l_hobby_matrix_c_array
+\array_clear:N \l_hobby_matrix_d_array
+\array_clear:N \l_hobby_vector_u_array
+\array_clear:N \l_hobby_psi_array
+\array_clear:N \l_hobby_theta_array
+\array_clear:N \l_hobby_phi_array
+\array_clear:N \l_hobby_sigma_array
+\array_clear:N \l_hobby_rho_array
+\array_clear:N \l_hobby_controla_array
+\array_clear:N \l_hobby_controlb_array
+\bool_set_false:N \l_hobby_closed_bool
+\bool_set_false:N \l_hobby_disjoint_bool
+
+ \int_set:Nn \l_hobby_npoints_int {-1}
+ \fp_set_eq:NN \l_hobby_in_angle_fp \c_undefined_fp
+ \fp_set_eq:NN \l_hobby_out_angle_fp \c_undefined_fp
+ \fp_set_eq:NN \l_hobby_in_curl_fp \c_one_fp
+ \fp_set_eq:NN \l_hobby_out_curl_fp \c_one_fp
+}
+\NewDocumentCommand \hobbyaddpoint { m } {
+ \keys_set:nn { hobby/read in all }
+ {
+ tension~out,
+ tension~in,
+ excess~angle,
+ #1
+ }
+ \array_push:Nx \l_hobby_tension_out_array {\fp_to_tl:N \l_hobby_tempc_fp}
+ \array_push:Nx \l_hobby_tension_in_array {\fp_to_tl:N \l_hobby_tempd_fp}
+ \array_push:Nx \l_hobby_excess_angle_array {\fp_to_tl:N \l_hobby_temps_fp}
+ \array_push:Nx \l_hobby_points_array {
+ x = \fp_use:N \l_hobby_tempa_fp,
+ y = \fp_use:N \l_hobby_tempb_fp }
+ \array_push:Nx \l_hobby_points_x_array {\fp_to_tl:N \l_hobby_tempa_fp}
+ \array_push:Nx \l_hobby_points_y_array {\fp_to_tl:N \l_hobby_tempb_fp}
+}
+\NewDocumentCommand \hobbysetparams { m } {
+ \keys_set:nn { hobby / read in params }
+ {
+ #1
+ }
+}
+\cs_new:Nn \hobby_set_cmds:nnn {
+ \cs_set_eq:NN \hobby_moveto:n #1
+ \cs_set_eq:NN \hobby_curveto:nnn #2
+ \cs_set_eq:NN \hobby_close:n #3
+}
+\tl_new:N \l_tmpc_tl
+\NewDocumentCommand \hobbygenpath { } {
+ \hobby_genpath:
+ \bool_if:NT \l_hobby_disjoint_bool {
+ \array_get:NnN \l_hobby_points_array {0} \l_tmpa_tl
+ \exp_args:No \hobby_moveto:n {\l_tmpa_tl}
+ }
+ \prg_stepwise_inline:nnnn {1} {1} {\l_hobby_npoints_int} {
+ \array_get:NnN \l_hobby_controla_array {##1} \l_tmpa_tl
+ \array_get:NnN \l_hobby_controlb_array {##1} \l_tmpb_tl
+ \array_get:NnN \l_hobby_points_array {##1} \l_tmpc_tl
+ \exp_args:Nooo \hobby_curveto:nnn {\l_tmpa_tl} {\l_tmpb_tl} {\l_tmpc_tl}
+}
+ \bool_if:NT \l_hobby_closed_bool {
+ \array_get:NnN \l_hobby_points_array {0} \l_tmpa_tl
+ \exp_args:No \hobby_close:n {\l_tmpa_tl}
+ }
+}
+\ExplSyntaxOff
+%%
+%% Copyright (C) 2012 by Andrew Stacey <stacey@math.ntnu.no>
+%%
+%% This file may be distributed and/or modified under the conditions
+%% of the LaTeX Project Public License, either version 1.3 of this
+%% license or (at your option) any later version.
+%% The latest version of this license is in:
+%%
+%% http://www.latex-project.org/lppl.txt
+%%
+%% and version 1.3 or later is part of all distributions of LaTeX
+%% version 2005/12/01 or later.
+%%
+%% This work is "maintained" (as per LPPL maintenance status) by
+%% Andrew Stacey.
+%%
+%% This work consists of the files hobby.dtx
+%% hobby_doc.tex
+%% and the derived files hobby.code.tex
+%% pgflibraryhobby.code.tex
+%% tikzlibraryhobby.code.tex
+%% hobby.ins
+%% hobby.pdf
+%% hobby_doc.pdf
+%% README.txt
+%%
+%%
+%% End of file `hobby.code.tex'.