Initial checkin

code/Makefile

@@ -0,0 +1,6 @@
+all:
+	cc -O3 -ansi -pedantic plain-knit.c -o plain-knit
+
+clean:
+	rm -f plain-knit
+

code/plain-knit.c

@@ -0,0 +1,248 @@
+#include <stdio.h>
+#include <math.h>
+
+struct Vector3
+{
+   double x;
+   double y;
+   double z;
+};
+
+double sqr( double x )
+{
+   return x*x;
+}
+
+double norm2( struct Vector3 v )
+{
+   return sqr(v.x) + sqr(v.y) + sqr(v.z);
+}
+
+double norm( struct Vector3 v )
+{
+   return sqrt( norm2( v ));
+}
+
+struct Vector3 scale( double c, struct Vector3 v )
+{
+   struct Vector3 cv;
+   cv.x = c * v.x;
+   cv.y = c * v.y;
+   cv.z = c * v.z;
+   return cv;
+}
+
+struct Vector3 cross( struct Vector3 u, struct Vector3 v )
+{
+   struct Vector3 w;
+   w.x = u.y*v.z - u.z*v.y;
+   w.y = u.z*v.x - u.x*v.z;
+   w.z = u.x*v.y - u.y*v.x;
+   return w;
+}
+
+struct Vector3 yarnCurve( double t, double a, double h, double d )
+{
+   struct Vector3 gamma_t;
+
+   gamma_t.x = t + a*sin(2.*t);
+   gamma_t.y = h * cos(t);
+   gamma_t.z = d * cos(2.*t);
+
+   return gamma_t;
+}
+
+void frenetFrame( double t, double a, double h, double d,
+                  struct Vector3* e1, struct Vector3* e2, struct Vector3* e3 )
+{
+   double u_t, v_t, x_t, y_t;
+
+   e1->x = 1. + 2.*a*cos(2.*t);
+   e1->y = -h*sin(t);
+   e1->z = -2.*d*sin(2.*t);
+
+   u_t = norm2(*e1);
+   v_t = 2.*h*h*cos(t)*sin(t) + 16.*d*d*cos(2.*t)*sin(2.*t) -
+         8.*a*(1. + 2.*a*cos(2.*t))*sin(2.*t);
+   x_t = 1./sqrt(u_t);
+   y_t = v_t/(2.*pow(u_t,3./2.));
+
+   e2->x = y_t*(-1. - 2.*a*cos(2.*t)) - x_t*4.*a*sin(2.*t);
+   e2->y = y_t*h*sin(t) - x_t*h*cos(t);
+   e2->z = y_t*2.*d*sin(2.*t) - x_t*4.*d*cos(2.*t);
+
+   *e1 = scale(  x_t, *e1 );
+   *e2 = scale( 1./norm(*e2), *e2 );
+   *e3 = cross( *e1, *e2 );
+}
+
+struct Vector3 fiberCurve( double t, double a, double h, double d,
+                           double r, double omega, double phi )
+{
+   struct Vector3 gamma_t;
+   struct Vector3 eta_t;
+   struct Vector3 e1, e2, e3;
+   double theta_t;
+
+   gamma_t = yarnCurve( t, a, h, d );
+   frenetFrame( t, a, h, d, &e1, &e2, &e3 );
+   theta_t = t*omega - 2.*cos(t) + phi;
+
+   eta_t.x = gamma_t.x + r*( cos(theta_t)*e2.x + sin(theta_t)*e3.x );
+   eta_t.y = gamma_t.y + r*( cos(theta_t)*e2.y + sin(theta_t)*e3.y );
+   eta_t.z = gamma_t.z + r*( cos(theta_t)*e2.z + sin(theta_t)*e3.z );
+
+   return eta_t;
+}
+
+void writeYarnCurves(
+      const char* filename, /* output filename */
+      int nRows, /* number of rows in wale direction */
+      double rowOffset, /* row spacing in wale direction */
+      int nLoops, /* number of loops in course direction */
+      int samplesPerLoop, /* sample points for each loop */
+      double a, /* loop roundness */
+      double h, /* loop height */
+      double d ) /* loop depth */
+{
+   double t;
+   int row, loop, sample;
+   int nPoints;
+   double dt, y0, t0;
+   struct Vector3 gamma_t;
+   FILE* out;
+
+   out = fopen( filename, "w" );
+
+   nPoints = 0;
+   dt = (2.*M_PI)/(double)samplesPerLoop;
+
+   /* write vertices */
+   for( row = 0; row < nRows; row++ )
+   {
+      y0 = rowOffset * (double)row;
+
+      for( loop = 0; loop < nLoops; loop++ )
+      {
+         t0 = 2.*M_PI * loop;
+         for( sample = 0; sample < samplesPerLoop; sample++ )
+         {
+            t = t0 + dt*(double)sample;
+
+            gamma_t = yarnCurve( t, a, h, d );
+
+            fprintf( out, "v %e %e %e\n",
+                  gamma_t.x,
+                  gamma_t.y + y0,
+                  gamma_t.z );
+         }
+      }
+   }
+
+   /* write polylines */
+   for( row = 0; row < nRows; row++ )
+   {
+      fprintf( out, "l" );
+      for( loop = 0; loop < nLoops; loop++ )
+      {
+         for( sample = 0; sample < samplesPerLoop; sample++ )
+         {
+            fprintf( out, " %d", nPoints+1 );
+            nPoints++;
+         }
+      }
+      fprintf( out, "\n" );
+   }
+   fclose( out );
+}
+
+void writeFiberCurves(
+      const char* filename, /* output filename */
+      int nRows, /* number of rows in wale direction */
+      double rowOffset, /* row spacing in wale direction */
+      int nLoops, /* number of loops in course direction */
+      int samplesPerLoop, /* sample points for each loop */
+      double a, /* loop roundness */
+      double h, /* loop height */
+      double d, /* loop depth */
+      double r, /* yarn radius */
+      double omega, /* amount of fiber twist */
+      int nFibers ) /* number of fibers around yarn */
+{
+   int row, fiber, loop, sample;
+   int nPoints;
+   double y0, t0;
+   double dt, dphi;
+   struct Vector3 eta_t;
+   FILE* out;
+
+   out = fopen( filename, "w" );
+
+   nPoints = 0;
+   dt = (2.*M_PI)/(double)samplesPerLoop;
+   dphi = (2.*M_PI)/(double)nFibers;
+
+   /* write vertices */
+   for( row = 0; row < nRows; row++ )
+   {
+      y0 = rowOffset * (double)row;
+
+      for( fiber = 0; fiber < nFibers; fiber++ )
+      {
+         double phi = dphi * (double)fiber;
+
+         for( loop = 0; loop < nLoops; loop++ )
+         {
+            t0 = 2.*M_PI * loop;
+            for( sample = 0; sample < samplesPerLoop; sample++ )
+            {
+               double t = t0 + dt*(double)sample;
+               eta_t = fiberCurve( t, a, h, d, r, omega, phi );
+               fprintf( out, "v %e %e %e\n", eta_t.x, y0 + eta_t.y, eta_t.z );
+            }
+         }
+      }
+   }
+
+   /* write polylines */
+   for( row = 0; row < nRows; row++ )
+   {
+      y0 = rowOffset * (double)row;
+
+      for( fiber = 0; fiber < nFibers; fiber++ )
+      {
+         fprintf( out, "l" );
+         for( loop = 0; loop < nLoops; loop++ )
+         {
+            for( sample = 0; sample < samplesPerLoop; sample++ )
+            {
+               fprintf( out, " %d", nPoints+1 );
+               nPoints++;
+            }
+         }
+         fprintf( out, "\n" );
+      }
+   }
+}
+
+int main( int argc, char** argv )
+{
+   const int nRows = 16;           /* number of rows generated */
+   const int nLoops = 12;          /* number of loops in each row */
+   const int samplesPerLoop = 64;  /* points sampled per period */
+   const int nFibers = 4;          /* number of twisted fibers */
+   const double a = 3/2.;          /* loop roundness */
+   const double d = 1.;            /* loop depth */
+   const double h = 4.;            /* loop height */
+   const double w = h + 1./2.;     /* row spacing */
+   const double r = 1./2.;         /* yarn radius */
+   const double omega = 5.;        /* fiber twist */
+   const double phi = M_PI/2.;     /* fiber offset */
+
+   writeYarnCurves( "yarn.obj", nRows, w, nLoops, samplesPerLoop, a, h, d );
+   writeFiberCurves( "fibers.obj", nRows, w, nLoops, samplesPerLoop, a, h, d,
+                     r, omega, nFibers );
+
+   return 0;
+}
+

note/Makefile

@@ -0,0 +1,14 @@
+FILE = YarnCurve
+
+all:
+	pdflatex -shell-escape $(FILE)
+	bibtex $(FILE)
+	pdflatex -shell-escape $(FILE)
+
+clean:
+	rm -f YarnCurve.aux
+	rm -f YarnCurve.bbl
+	rm -f YarnCurve.blg
+	rm -f YarnCurve.log
+	rm -f YarnCurve.pdf
+	rm -rf _minted-YarnCurve

note/YarnCurve.bib

@@ -0,0 +1,116 @@
+@article{yuksel2012stitch,
+  title={Stitch meshes for modeling knitted clothing with yarn-level detail},
+  author={Yuksel, Cem and Kaldor, Jonathan M and James, Doug L and Marschner, Steve},
+  journal={ACM Transactions on Graphics (TOG)},
+  volume={31},
+  number={4},
+  pages={1--12},
+  year={2012},
+  publisher={ACM New York, NY, USA}
+}
+
+@incollection{kaldor2010efficient,
+  title={Efficient yarn-based cloth with adaptive contact linearization},
+  author={Kaldor, Jonathan M and James, Doug L and Marschner, Steve},
+  booktitle={ACM SIGGRAPH 2010 papers},
+  pages={1--10},
+  year={2010}
+}
+
+@article{wadekar2020geometric,
+  title={Geometric modeling of knitted fabrics using helicoid scaffolds},
+  author={Wadekar, Paras and Goel, Prateek and Amanatides, Chelsea and Dion, Genevieve and Kamien, Randall D and Breen, David E},
+  journal={Journal of Engineered Fibers and Fabrics},
+  volume={15},
+  pages={1558925020913871},
+  year={2020},
+  publisher={SAGE Publications Sage UK: London, England}
+}
+
+@article{gonzalez1999global,
+  title={Global curvature, thickness, and the ideal shapes of knots},
+  author={Gonzalez, Oscar and Maddocks, John H},
+  journal={Proceedings of the National Academy of Sciences},
+  volume={96},
+  number={9},
+  pages={4769--4773},
+  year={1999},
+  publisher={National Acad Sciences}
+}
+
+@incollection{ashton2005fast,
+  title={A fast octree-based algorithm for computing ropelength},
+  author={Ashton, Ted and Cantarella, Jason},
+  booktitle={Physical And Numerical Models In Knot Theory: Including Applications to the Life Sciences},
+  pages={323--341},
+  year={2005},
+  publisher={World Scientific}
+}
+
+@article{Leaf:1955:GPK,
+  title={The geometry of a plain knitted loop},
+  author={Leaf, GAV and Glaskin, A},
+  journal={Journal of the Textile Institute Transactions},
+  volume={46},
+  number={9},
+  pages={T587--T605},
+  year={1955},
+  publisher={Taylor \& Francis}
+}
+
+@article{Munden:1959:GDP,
+  title={The geometry and dimensional properties of plain-knit fabrics},
+  author={Munden, DL},
+  journal={Journal of the Textile Institute Transactions},
+  volume={50},
+  number={7},
+  pages={T448--T471},
+  year={1959},
+  publisher={Taylor \& Francis}
+}
+
+@article{Peirce:1947:GPA,
+  title={Geometrical principles applicable to the design of functional fabrics},
+  author={Peirce, Frederick Thomas},
+  journal={Textile Research Journal},
+  volume={17},
+  number={3},
+  pages={123--147},
+  year={1947},
+  publisher={Sage Publications Sage CA: Thousand Oaks, CA}
+}
+
+@article{Chamberlain:1926:HYF,
+  title={Hosiery Yarns and Fabrics},
+  author={J. Chamberlain},
+  year={1926},
+  publisher={J. W. Hemming \& Capey, Leicester}
+}
+
+@article{zhao2016fitting,
+  title={Fitting procedural yarn models for realistic cloth rendering},
+  author={Zhao, Shuang and Luan, Fujun and Bala, Kavita},
+  journal={ACM Transactions on Graphics (TOG)},
+  volume={35},
+  number={4},
+  pages={1--11},
+  year={2016},
+  publisher={ACM New York, NY, USA}
+}
+
+@incollection{jakob2010radiative,
+  title={A radiative transfer framework for rendering materials with anisotropic structure},
+  author={Jakob, Wenzel and Arbree, Adam and Moon, Jonathan T and Bala, Kavita and Marschner, Steve},
+  booktitle={ACM SIGGRAPH 2010 papers},
+  pages={1--13},
+  year={2010}
+}
+
+@inproceedings{xu2001photorealistic,
+  title={Photorealistic rendering of knitwear using the lumislice},
+  author={Xu, Ying-Qing and Chen, Yanyun and Lin, Stephen and Zhong, Hua and Wu, Enhua and Guo, Baining and Shum, Heung-Yeung},
+  booktitle={Proceedings of the 28th annual conference on Computer graphics and interactive techniques},
+  pages={391--398},
+  year={2001}
+}
+