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Player Sessions Completed - working project at this point
2026-04-07 06:36:11 -04:00
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D<00>E<08>Px<50><78>3<EFBFBD>M<EFBFBD><4D><EFBFBD><1A><><1A>o,<00>|x// Parametric Torus Knot
float c_add_a_mul_cosv = float(c + a * cosv);
Torus.x = c_add_a_mul_cosv * cosu;
Torus.y = c_add_a_mul_cosv * sinu;
Torus.z = a * sinv;
//First Derivative
//int psq = int(p*p);
//int qsq = int(q*q);
float psq = float(p*p);
float qsq = float(q*q);
float a_mul_cosv_add_c = float(a * cosv + c);
float a_mul_p_mul_sinv = float(a * p * sinv);
TorusTangent.x = float(-q * a_mul_cosv_add_c * sinu - a_mul_p_mul_sinv * cosu);
TorusTangent.y = float(q * a_mul_cosv_add_c * cosu - a_mul_p_mul_sinv * sinu);
TorusTangent.z = float(a * p * cosv);
TorusTangent = normalize(TorusTangent);
// Second Derivative
// This tells us the curvature and points in the direction of highest curvature, so
// we negate it to generate a "surface normal" which represents the normal of the
// underlying torus gometry underneath the knot
float a_mul_p_mul_q_mul_sinv = float(a * p * q * sinv);
float a_mul_qsq = float(a * qsq);
float a_mul_psq = float(a * psq);
TorusNormal.x = -float( 2 * a_mul_p_mul_q_mul_sinv * sinu + ((-a_mul_qsq - a_mul_psq) * cosv -c * qsq ) * cosu );
TorusNormal.y = -float( -((a_mul_qsq + a_mul_psq) * cosv + c * qsq ) * sinu - 2 * a_mul_p_mul_q_mul_sinv * cosu );
TorusNormal.z = -float( -a_mul_psq * sinv );
TorusNormal = normalize(TorusNormal);
// Bitangent vs. Binormal depends on how we view the surface, as a curve or a mesh.
// At this point it's actually a Binormal, but we will express this with an optional radial projection
// which would make a surface, at which time its a bitangent. We will roll with it :)
TorusBitangent = cross(TorusNormal, TorusTangent);<00><00>a<00>P <00>f<00> "v<00><><EFBFBD><EFBFBD><EFBFBD><00>Co"v<00><><EFBFBD><EFBFBD><EFBFBD><00>Co*"v<00><><EFBFBD><EFBFBD><EFBFBD><00>Co<00>"v<00><><EFBFBD><EFBFBD><EFBFBD><00>Co+"v<00><><EFBFBD><EFBFBD><EFBFBD><00>Co<00>"v<00><><EFBFBD><EFBFBD><EFBFBD><00>Co<00>"v<00><><EFBFBD><EFBFBD><EFBFBD><00>Coz"v<00><><EFBFBD><EFBFBD><EFBFBD><00>Co<00>"v<00><><EFBFBD><EFBFBD><EFBFBD><00>Coy <00>g<00><00>"v<00><><EFBFBD><EFBFBD><EFBFBD><00>Co<00>"v<00><><EFBFBD><EFBFBD><EFBFBD><00>Co<00>"v<00><><EFBFBD><EFBFBD><EFBFBD><00>Co<00>"v<00><><EFBFBD><EFBFBD><EFBFBD><00>Coo!<00>E<08>O{<7B>e"9D<39>>?<3F>Χ<>lR<00><><EFBFBD><EFBFBD>mR0<><30><EFBFBD>i<00>40Parametric Torus Knot, plus partial derivitivesk<00>E<08>Co<43><6F><EFBFBD>H<EFBFBD>O<EFBFBD>GF<47><04>o<13><>~eF<65>s<EFBFBD>f<EFBFBD>l <20><13><>~eF<65>s<EFBFBD>f<EFBFBD>l <20><00><00><><EFBFBD><EFBFBD><00>o<00><><EFBFBD><EFBFBD>o<00>4P<34>hgG<67>C<EFBFBD><43><EFBFBD><EFBFBD><EFBFBD><EFBFBD><02> <0A><><0E>.J<>.<2E><07>gt' <0A><><0E>.J<>.<2E><07>gt'<00><00><><EFBFBD><EFBFBD><00>o<00><><EFBFBD><EFBFBD>o<00>[<11><><EFBFBD>gD<67><44><EFBFBD><EFBFBD><EFBFBD><EFBFBD>#<00><14><><EFBFBD>/<2F>N<EFBFBD>pI<70>P<EFBFBD><<3C><00><14><><EFBFBD>/<2F>N<EFBFBD>pI<70>P<EFBFBD><<3C>*<00><00><><EFBFBD><EFBFBD><00>o<00><><EFBFBD><EFBFBD>o<00>.<2E><18><><EFBFBD>$F<>e<EFBFBD>o/<1F>8<00><><EFBFBD>ґ%<25>@<40>ߓf<DF93><66><16><00><><EFBFBD>ґ%<25>@<40>ߓf<DF93><66><16><><00><00><><EFBFBD><EFBFBD><00>o<00><><EFBFBD><EFBFBD>o<00> <00><>!<21>^<5E><>H<EFBFBD><48><EFBFBD>b<EFBFBD>m`<00><><EFBFBD><EFBFBD>殂K<E6AE82><4B>4S?<3F><>I<00><><EFBFBD><EFBFBD>殂K<E6AE82><4B>4S?<3F><>I+<00><00><><EFBFBD><EFBFBD><00>o<00><><EFBFBD><EFBFBD>o<00> <20>Gi<47>]<5D>L<EFBFBD>q <09>r,<2C>NjVe$]<5D>@<40>%Q󥦝jVe$]<5D>@<40>%Q󥦝<00><00><00><><EFBFBD><EFBFBD><00>o<00><><EFBFBD><EFBFBD>o<00>
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b<><62><EFBFBD>98<39>O<EFBFBD><4F><1F>\) <00><>UL<55><4C><EFBFBD>K<EFBFBD><4B>Qh}g/<2F> <00><>UL<55><4C><EFBFBD>K<EFBFBD><4B>Qh}g/<2F><00><00><><EFBFBD><EFBFBD>1Value in which a complete rotation has occurred.<00>o<00><><EFBFBD><EFBFBD>o1.01.0<00> <00><>!<21>^<5E><>H<EFBFBD><48><EFBFBD>b<EFBFBD>m` <00><>!<21>^<5E><>H<EFBFBD><48><EFBFBD>b<EFBFBD>m`<04><00><00><><EFBFBD><EFBFBD>Result<01>o<00><><EFBFBD><EFBFBD>o<00><00><><EFBFBD>ґ%<25>@<40>ߓf<DF93><66><16>w^s!<00>Ez)Κ<><J<>LE9<45><39>/zlR<00><><EFBFBD><EFBFBD>mR<00>i<00>qtk<00>E<08>L&U<13>SE<53><45>T<EFBFBD><54>6<EFBFBD>to
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<00><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>B<EFBFBD><42><EFBFBD><14><>d)
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b<><62><EFBFBD>98<39>O<EFBFBD><4F><1F>\)
b<><62><EFBFBD>98<39>O<EFBFBD><4F><1F>\)<29><00><00><><EFBFBD><EFBFBD>Result<01>o<00><><EFBFBD><EFBFBD>o<00>=šf-xE<78>y<EFBFBD><79><EFBFBD><0F>{ <00><>f0+E<><45>L7<4C>fU0
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e<><65>\<5C>{F<><46>F<07>t<EFBFBD><74><00><00><><EFBFBD><EFBFBD>\2o<00>w^s!<00>E<08><13>)q:C<>1<EFBFBD>Qs:<3A><>lR<00><><EFBFBD><EFBFBD>mR<00>i<00>ptk<00>E5<>d?<3F><>J<><4A>O<EFBFBD><4F><EFBFBD><EFBFBD>o r<03>G<EFBFBD><47><EFBFBD>O<EFBFBD>jL<1C>j<EFBFBD><6A> r<03>G<EFBFBD><47><EFBFBD>O<EFBFBD>jL<1C>j<EFBFBD><6A><00><00><><EFBFBD><EFBFBD>A<00>o<00><><EFBFBD><EFBFBD>o1.01.0<00><00>T'}~><3E>L<EFBFBD><4C><EFBFBD>Ͽ<EFBFBD> <00><>_<EFBFBD><5F>jXF<58><46><EFBFBD>7<EFBFBD><37>)<29> <00><>_<EFBFBD><5F>jXF<58><46><EFBFBD>7<EFBFBD><37>)<29> <00><00><><EFBFBD><EFBFBD>B<00>o<00><><EFBFBD><EFBFBD>o1.01.0<00>=l<>R<EFBFBD>:H<><48><EFBFBD>v <05> <00>4<EFBFBD><34>+<2B>F<><46><EFBFBD>/L<>7 <00>4<EFBFBD><34>+<2B>F<><46><EFBFBD>/L<>7<1D><00><00><><EFBFBD><EFBFBD>Result<01>o<00><><EFBFBD><EFBFBD>o<00> <00>і1wkM<>F|dns0 處<><E89995>r%E<>,pѓy<D193><79> <00><><08><><16>G<EFBFBD><03>o\1<> <00><><08><><16>G<EFBFBD><03>o\1<><00><00><><EFBFBD><EFBFBD>\2o<00>w^r!<00>E2<><32><14>M<EFBFBD>E<EFBFBD>qqHc<1E>lR<00><><EFBFBD><EFBFBD>mR<00>i<00>
cos vk<00>E<08>bO<62>~<7E>C<EFBFBD><43><EFBFBD>]n<><6E>Ro <00>і1wkM<>F|dns0 <00>і1wkM<>F|dns0
<00><00><><EFBFBD><EFBFBD>(Angle as specified by the period range.<00>o<00><><EFBFBD><EFBFBD>o1.01.0<00> <00>4<EFBFBD><34>+<2B>F<><46><EFBFBD>/L<>7 A<><41>F<EFBFBD>{PJ<50><4A>N<><4E>5x A<><41>F<EFBFBD>{PJ<50><4A>N<><4E>5x<00><00><><EFBFBD><EFBFBD>1Value in which a complete rotation has occurred.<00>o<00><><EFBFBD><EFBFBD>o1.01.0<00> <20>Gi<47>]<5D>L<EFBFBD>q <09>r,<2C>N <20>Gi<47>]<5D>L<EFBFBD>q <09>r,<2C>N<EFBFBD><00><00><><EFBFBD><EFBFBD>Result<01>o<00><><EFBFBD><EFBFBD>o<00><00><><EFBFBD><EFBFBD>殂K<E6AE82><4B>4S?<3F><>Iw^t!<00>E<08>_Rq<52>bG<62><47>J<EFBFBD>4-lR<00><><EFBFBD><EFBFBD>mR i<00> sine vk<00>E<08><><EFBFBD><EFBFBD>k<EFBFBD>rF<72><46><EFBFBD>\<5C>4 <20>o 處<><E89995>r%E<>,pѓy<D193><79> 處<><E89995>r%E<>,pѓy<D193><79>
<00><00><><EFBFBD><EFBFBD>(Angle as specified by the period range.<00>o<00><><EFBFBD><EFBFBD>o1.01.0<00> <00>4<EFBFBD><34>+<2B>F<><46><EFBFBD>/L<>7 1ЗS<D097>T@<40>@Ojb<6A>^ 1ЗS<D097>T@<40>@Ojb<6A>^<00><00><><EFBFBD><EFBFBD>1Value in which a complete rotation has occurred.<00>o<00><><EFBFBD><EFBFBD>o1.01.0<00>
<EFBFBD>ij<EFBFBD><EFBFBD>D<EFBFBD><EFBFBD>N<EFBFBD>X<EFBFBD><EFBFBD><EFBFBD>
<EFBFBD>ij<EFBFBD><EFBFBD>D<EFBFBD><EFBFBD>N<EFBFBD>X<EFBFBD><EFBFBD><EFBFBD><EFBFBD><00><00><><EFBFBD><EFBFBD>Result<01>o<00><><EFBFBD><EFBFBD>o<00>jVe$]<5D>@<40>%Q󥦝w^r!<00>EG<><47><EFBFBD><EFBFBD>ڔO<DA94>ש<><D7A9> <0C>lR<00><><EFBFBD><EFBFBD>mR<00>i<00>
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<00><00><><EFBFBD><EFBFBD>(Angle as specified by the period range.<00>o<00><><EFBFBD><EFBFBD>o1.01.0<00>
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