2 * Equation for a Moebius strip
11 Point MoebiusStrip::edgepoint(double t) {
12 double theta= (t-0.5)*4.0*M_PI;
13 double r= 1.0 - halfgap*(1.0 - sin(theta/2.0));
14 return Point(r*sin(theta),
16 halfbreadth*cos(theta/2.0));
19 Point MoebiusStrip::middlepoint(double t, double u) {
20 return edgepoint(t*0.5)*u + edgepoint((t+1)*0.5)*(1.0-u);
26 Bezier(double x0, double x1, double dx0, double dx1);
27 double operator()(double t) { return h + t*(g + t*(f + t*e)); }
31 Bezier::Bezier(double x0, double x1, double dx0, double dx1) {
32 // e= 2*x0 - 2*x1 + dx0 + dx1;
33 // f= x1 - dx0 - x0 - e;
36 e= g + 2*h + dx1 - 2*x1;
40 void Bezier::debug() {
41 fprintf(stderr,"bz e %7.4f f %7.4f g %7.4f h %7.4f\n",e,f,g,h);
44 // The first end is at [sin(theta/2),-cos(theta/2),0]
45 // The second end is at [-theta/pi,0,sin(theta)]
46 // The first end is oriented towards [0,cos(theta),sin(theta)]
47 // The second end is oriented towards [0,-1,0]
49 Point MoebiusEnfoldmentAny::edgepoint(double t) {
50 double theta= t*2.0*M_PI;
51 return Point(sin(theta),cos(theta),0);
54 Point MoebiusEnfoldment::middlepoint(double t, double u) {
55 if (t > bottomportion) {
57 t /= (1.0 - bottomportion);
58 double sizehere= sqrt(1-t*t);
59 return Point((u*2.0-1.0) * sizehere,
61 sizehere * thickness * sin(u*2.0*M_PI));
64 double theta= (.5-u)*2*M_PI;
65 Bezier bx(sin(theta*.5), -theta/M_PI, 0, 0);
66 double ypushiness= (1-cos(theta))*2.5+1;
67 // double fudge= (M_PI*sin(theta*.5)*cos(theta*.5))*(.5-u)*(.5-u)*4;
68 double fudge= (.5-u)*(.5-u)*4*cos(theta*.5);
69 Bezier by(-cos(theta*.5), 0,
70 cos(theta)*ypushiness + fudge*ypushiness,
73 Bezier bz(0, sin(theta), sin(theta), 0);
74 return Point( bx(t), by(t), thickness * bz(t) );
78 Point MoebiusEnfoldmentNew::middlepoint(double t, double u) {
81 double sin_pi_t= sin(M_PI*t);
82 double cos_pi_t= cos(M_PI*t);
83 double sin_2pi_t= sin(2.0*M_PI*t);
84 double cos_2pi_t= cos(2.0*M_PI*t);
86 double prop_circ= 0.5+0.5*cos(2.0*M_PI*u);
87 // double prop_circ= 1.0-2.0*u;
89 Point p_edge(-sin_pi_t,cos_pi_t,0);
91 double alpha_circ= (2.0*M_PI)*(2.0*t)*(2.0*u);
92 Point v_edge1(cos_2pi_t*sin_pi_t,-cos_2pi_t*cos_pi_t,sin_2pi_t);
93 Point v_edge2(sin_2pi_t*cos_pi_t,-sin_2pi_t*sin_pi_t,-cos_2pi_t);
94 Point p_circ_cent= p_edge + v_edge2*(2.0*t);
95 Point p_circ_pt= p_circ_cent + (v_edge1*sin(alpha_circ) + v_edge2*-cos(alpha_circ))*(2.0*t);
96 p_circ_pt[1]= p_edge[1];
98 Point v_line(-cos_pi_t,0,sin_pi_t);
99 Point p_line_start(0,1.0-2.0*t,0);
100 Point p_line_pt= p_line_start + v_line*(1.0-2.0*u)*(M_PI*t);
102 return p_circ_pt*prop_circ + p_line_pt*(1.0-prop_circ);
104 return middlepoint(0.5,u) + Point(0,0.5-t,0);
107 Point p_mirror= middlepoint(t,1.0-u);
108 return Point(-p_mirror[0], p_mirror[1], -p_mirror[2]);