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https://github.com/zenorogue/hyperrogue.git
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fixed raycaster in twisted geometries; weirdly twisted spherical geometry
This commit is contained in:
Zeno Rogue
parent
191ef35d21
commit
0926b98c83
@ -1300,7 +1300,7 @@ EX hyperpoint tangent_length(hyperpoint dir, ld length) {
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EX hyperpoint direct_exp(hyperpoint v) {
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if(sn::in()) return nisot::numerical_exp(v);
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if(nil) return nilv::formula_exp(v);
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if(sl2 || stretch::in()) return rots::formula_exp(v);
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if(sl2 || stretch::in()) return stretch::mstretch ? nisot::numerical_exp(v) : rots::formula_exp(v);
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if(prod) return product::direct_exp(v);
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ld d = hypot_d(GDIM, v);
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if(d > 0) for(int i=0; i<GDIM; i++) v[i] = v[i] * sin_auto(d) / d;
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164
nonisotropic.cpp
164
nonisotropic.cpp
@ -2280,14 +2280,101 @@ EX }
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/** stretched rotation space (S3 or SLR) */
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EX namespace stretch {
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EX ld factor;
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EX ld factor;
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EX bool mstretch;
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EX transmatrix m_itoa, m_atoi, m_pd;
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EX ld ms_christoffel[3][3][3];
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EX void enable_mstretch() {
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mstretch = true;
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for(int a=0; a<4; a++)
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for(int b=0; b<4; b++)
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if(a==3 || b==3) m_atoi[a][b] = (a==b);
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m_itoa = inverse3(m_atoi);
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for(int a=0; a<4; a++)
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for(int b=0; b<4; b++)
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if(a==3 || b==3)
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m_itoa[a][b] = m_atoi[a][b] = 0;
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for(int j=0; j<3; j++)
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for(int k=0; k<3; k++) {
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m_pd[j][k] = 0;
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for(int i=0; i<3; i++)
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m_pd[j][k] += m_atoi[i][j] * m_atoi[i][k];
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}
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auto& c = ms_christoffel;
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ld A00 = m_pd[0][0];
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ld A11 = m_pd[1][1];
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ld A22 = m_pd[2][2];
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ld A01 = m_pd[0][1] + m_pd[1][0];
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ld A02 = m_pd[0][2] + m_pd[2][0];
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ld A12 = m_pd[2][1] + m_pd[1][2];
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ld B01 = A01 * A01;
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ld B02 = A02 * A02;
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ld B12 = A12 * A12;
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ld B00 = A00 * A00;
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ld B11 = A11 * A11;
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ld B22 = A22 * A22;
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ld den = (-4*A00*A11*A22 + A00*B12 + B01*A22 - A01*A02*A12 + B02*A11);
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/* to do: these formulas are not correct for SL; also the engine currently depends on rotational symmetry, which may not hold */
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c[ 0 ][ 0 ][ 0 ] = (A01*(A01*A12 - 2*A02*A11) + A02*(2*A01*A22 - A02*A12))/den ;
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c[ 0 ][ 0 ][ 1 ] = (A02*(4*A11*A22 - B12)/2 + A12*(2*A01*A22 - A02*A12)/2 - (A00 - A11)*(A01*A12 - 2*A02*A11))/den ;
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c[ 0 ][ 0 ][ 2 ] = (-A01*(4*A11*A22 - B12)/2 + A12*(A01*A12 - 2*A02*A11)/2 - (A00 - A22)*(2*A01*A22 - A02*A12))/den ;
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c[ 0 ][ 1 ][ 0 ] = (A02*(4*A11*A22 - B12)/2 + A12*(2*A01*A22 - A02*A12)/2 - (A00 - A11)*(A01*A12 - 2*A02*A11))/den ;
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c[ 0 ][ 1 ][ 1 ] = (-A01*(A01*A12 - 2*A02*A11) + A12*(4*A11*A22 - B12))/den ;
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c[ 0 ][ 1 ][ 2 ] = (B01*A22 - B02*A11 + 4*B11*A22 - A11*B12 - 4*A11*B22 + B12*A22)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
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c[ 0 ][ 2 ][ 0 ] = (-A01*(4*A11*A22 - B12)/2 + A12*(A01*A12 - 2*A02*A11)/2 - (A00 - A22)*(2*A01*A22 - A02*A12))/den ;
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c[ 0 ][ 2 ][ 1 ] = (B01*A22 - B02*A11 + 4*B11*A22 - A11*B12 - 4*A11*B22 + B12*A22)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
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c[ 0 ][ 2 ][ 2 ] = -(A02*(2*A01*A22 - A02*A12) + A12*(4*A11*A22 - B12))/den ;
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c[ 1 ][ 0 ][ 0 ] = -(A01*(2*A00*A12 - A01*A02) + A02*(4*A00*A22 - B02))/den ;
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c[ 1 ][ 0 ][ 1 ] = (-A02*(2*A01*A22 - A02*A12)/2 - A12*(4*A00*A22 - B02)/2 + (A00 - A11)*(2*A00*A12 - A01*A02))/den ;
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c[ 1 ][ 0 ][ 2 ] = (-4*B00*A22 + A00*B02 + A00*B12 + 4*A00*B22 - B01*A22 - B02*A22)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
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c[ 1 ][ 1 ][ 0 ] = (-A02*(2*A01*A22 - A02*A12)/2 - A12*(4*A00*A22 - B02)/2 + (A00 - A11)*(2*A00*A12 - A01*A02))/den ;
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c[ 1 ][ 1 ][ 1 ] = (A01*(2*A00*A12 - A01*A02) - A12*(2*A01*A22 - A02*A12))/den ;
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c[ 1 ][ 1 ][ 2 ] = (A01*(4*A00*A22 - B02)/2 + A02*(2*A00*A12 - A01*A02)/2 + (A11 - A22)*(2*A01*A22 - A02*A12))/den ;
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c[ 1 ][ 2 ][ 0 ] = (-4*B00*A22 + A00*B02 + A00*B12 + 4*A00*B22 - B01*A22 - B02*A22)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
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c[ 1 ][ 2 ][ 1 ] = (A01*(4*A00*A22 - B02)/2 + A02*(2*A00*A12 - A01*A02)/2 + (A11 - A22)*(2*A01*A22 - A02*A12))/den ;
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c[ 1 ][ 2 ][ 2 ] = (A02*(4*A00*A22 - B02) + A12*(2*A01*A22 - A02*A12))/den ;
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c[ 2 ][ 0 ][ 0 ] = (A01*(4*A00*A11 - B01) + A02*(2*A00*A12 - A01*A02))/den ;
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c[ 2 ][ 0 ][ 1 ] = (4*B00*A11 - A00*B01 - 4*A00*B11 - A00*B12 + B01*A11 + B02*A11)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
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c[ 2 ][ 0 ][ 2 ] = (-A01*(A01*A12 - 2*A02*A11)/2 + A12*(4*A00*A11 - B01)/2 - (A00 - A22)*(2*A00*A12 - A01*A02))/den ;
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c[ 2 ][ 1 ][ 0 ] = (4*B00*A11 - A00*B01 - 4*A00*B11 - A00*B12 + B01*A11 + B02*A11)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
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c[ 2 ][ 1 ][ 1 ] = (-A01*(4*A00*A11 - B01) + A12*(A01*A12 - 2*A02*A11))/den ;
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c[ 2 ][ 1 ][ 2 ] = (A00*A01*A12 + 2*A00*A02*A11 - B01*A02 + A01*A11*A12 - A01*A12*A22 - 2*A02*B11 + 2*A02*A11*A22)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
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c[ 2 ][ 2 ][ 0 ] = (-A01*(A01*A12 - 2*A02*A11)/2 + A12*(4*A00*A11 - B01)/2 - (A00 - A22)*(2*A00*A12 - A01*A02))/den ;
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c[ 2 ][ 2 ][ 1 ] = (A00*A01*A12 + 2*A00*A02*A11 - B01*A02 + A01*A11*A12 - A01*A12*A22 - 2*A02*B11 + 2*A02*A11*A22)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
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c[ 2 ][ 2 ][ 2 ] = -(A02*(2*A00*A12 - A01*A02) + A12*(A01*A12 - 2*A02*A11))/den ;
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for(int i=0; i<3; i++)
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for(int j=0; j<3; j++)
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for(int k=0; k<3; k++)
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if(c[i][j][k])
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println(hlog, tie(i,j,k), " : ", c[i][j][k]);
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println(hlog, "ATOI = ", m_atoi);
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println(hlog, "ITOA = ", m_itoa, " vs ", 1/not_squared());
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println(hlog, "PD = ", m_pd, " vs ", factor);
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ray::reset_raycaster();
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}
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EX bool applicable() {
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return rotspace || among(geometry, gCell120, gECell120, gCell24, gECell24, gCell8, gECell8);
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}
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EX bool in() {
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return factor && applicable();
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return (factor || mstretch) && applicable();
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}
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EX transmatrix translate(hyperpoint h) {
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@ -2308,26 +2395,32 @@ EX namespace stretch {
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return translate(h);
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}
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hyperpoint mulz(const hyperpoint at, const hyperpoint velocity, ld factor) {
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hyperpoint mulz(const hyperpoint at, const hyperpoint velocity, ld zf) {
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auto vel = itranslate(at) * velocity;
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vel[2] *= factor;
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vel[2] *= zf;
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return translate(at) * vel;
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}
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EX ld squared() {
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return abs(1 + factor);
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}
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EX ld not_squared() {
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return sqrt(squared());
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}
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EX hyperpoint isometric_to_actual(const hyperpoint at, const hyperpoint velocity) {
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return mulz(at, velocity, 1/not_squared());
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if(mstretch)
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return translate(at) * m_itoa * itranslate(at) * velocity;
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else
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return mulz(at, velocity, 1/not_squared());
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}
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EX hyperpoint actual_to_isometric(const hyperpoint at, const hyperpoint velocity) {
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return mulz(at, velocity, not_squared());
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if(mstretch)
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return translate(at) * m_atoi * itranslate(at) * velocity;
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else
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return mulz(at, velocity, not_squared());
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}
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EX hyperpoint christoffel(const hyperpoint at, const hyperpoint velocity, const hyperpoint transported) {
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@ -2337,15 +2430,22 @@ EX namespace stretch {
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hyperpoint c;
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auto K = factor;
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if(!sphere) K = -2 - K;
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c[0] = -K * (vel[1] * tra[2] + vel[2] * tra[1]);
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c[1] = K * (vel[0] * tra[2] + vel[2] * tra[0]);
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c[2] = 0;
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c[3] = 0;
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if(mstretch) {
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c = Hypc;
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for(int i=0; i<3; i++)
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for(int j=0; j<3; j++)
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for(int k=0; k<3; k++)
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c[i] += vel[j] * tra[k] * ms_christoffel[i][j][k];
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}
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else {
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auto K = factor;
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c[0] = (sphere ? -K : K+2) * (vel[1] * tra[2] + vel[2] * tra[1]);
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c[1] = (sphere ? K : -(K+2)) * (vel[0] * tra[2] + vel[2] * tra[0]);
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c[2] = 0;
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c[3] = 0;
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}
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return translate(at) * c;
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}
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@ -2591,7 +2691,14 @@ EX namespace nisot {
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auto fix = [&] (hyperpoint& h, ld& m) {
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h = stretch::itranslate(at) * h;
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h[3] = 0;
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ld m1 = h[0] * h[0] + h[1] * h[1] + h[2] * h[2] * stretch::squared();
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ld m1;
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if(stretch::mstretch) {
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m1 = 0;
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for(int i=0; i<3; i++) for(int j=0; j<3; j++)
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m1 += h[i] * stretch::m_pd[i][j] * h[j];
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}
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else
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m1 = h[0] * h[0] + h[1] * h[1] + h[2] * h[2] * stretch::squared();
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h /= sqrt(m1/m);
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h = stretch::translate(at) * h;
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};
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@ -2746,6 +2853,29 @@ EX namespace nisot {
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shift_arg_formula(stretch::factor, ray::reset_raycaster);
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return 0;
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}
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else if(argis("-mstretch")) {
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PHASEFROM(2);
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auto& M = stretch::m_atoi;
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M = Id;
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while(true) {
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shift();
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string s = args();
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if(isize(s) == 2 && among(s[0], 'a', 'b','c') && among(s[1], 'a', 'b', 'c'))
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shift_arg_formula(M[s[0]-'a'][s[1]-'a'], stretch::enable_mstretch);
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else break;
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}
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// shift_arg_formula(stretch::yfactor, ray::reset_raycaster);
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return 0;
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}
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else if(argis("-mstretch1")) {
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PHASEFROM(2);
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auto& M = stretch::m_atoi;
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M = Id;
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M[2][2] = stretch::not_squared();
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stretch::enable_mstretch();
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// shift_arg_formula(stretch::yfactor, ray::reset_raycaster);
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return 0;
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}
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else if(argis("-prodturn")) {
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PHASEFROM(2);
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if(prod) stop_game();
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117
raycaster.cpp
117
raycaster.cpp
@ -108,6 +108,7 @@ struct raycaster : glhr::GLprogram {
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GLint uBLevel;
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GLint uPosX, uPosY;
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GLint uWallOffset, uSides;
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GLint uITOA, uATOI;
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raycaster(string vsh, string fsh);
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};
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@ -151,6 +152,9 @@ raycaster::raycaster(string vsh, string fsh) : GLprogram(vsh, fsh) {
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uPosX = glGetUniformLocation(_program, "uPosX");
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uPosY = glGetUniformLocation(_program, "uPosY");
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uITOA = glGetUniformLocation(_program, "uITOA");
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uATOI = glGetUniformLocation(_program, "uATOI");
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}
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shared_ptr<raycaster> our_raycaster;
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@ -388,8 +392,17 @@ void enable_raycaster() {
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if(stretch::in()) {
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fmain +=
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"tangent = s_itranslate(position) * tangent;\n"
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"tangent[2] /= " + to_glsl(stretch::not_squared()) + ";\n"
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"tangent = s_itranslate(position) * tangent;\n";
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if(stretch::mstretch) {
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fsh += "mediump uniform mat4 uITOA;\n";
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fsh += "mediump uniform mat4 uATOI;\n";
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fmain +=
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"tangent = uITOA * tangent;\n";
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}
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else
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fmain +=
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"tangent[2] /= " + to_glsl(stretch::not_squared()) + ";\n";
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fmain +=
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"tangent = s_translate(position) * tangent;\n";
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;
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}
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@ -576,23 +589,40 @@ void enable_raycaster() {
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" }\n";
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use_christoffel = false;
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}
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else if(sl2) {
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fsh += "mediump mat4 s_translate(vec4 h) {\n"
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"return mat4(h.w,h.z,h.y,h.x,-h.z,h.w,-h.x,h.y,h.y,-h.x,h.w,-h.z,h.x,h.y,h.z,h.w);\n"
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"}\n";
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else if(sl2 || stretch::in()) {
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if(sl2) {
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fsh += "mediump mat4 s_translate(vec4 h) {\n"
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"return mat4(h.w,h.z,h.y,h.x,-h.z,h.w,-h.x,h.y,h.y,-h.x,h.w,-h.z,h.x,h.y,h.z,h.w);\n"
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"}\n";
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}
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else {
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fsh += "mediump mat4 s_translate(vec4 h) {\n"
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"return mat4(h.w,h.z,-h.y,-h.x,-h.z,h.w,h.x,-h.y,h.y,-h.x,h.w,-h.z,h.x,h.y,h.z,h.w);\n"
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"}\n";
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}
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fsh += "mediump mat4 s_itranslate(vec4 h) {\n"
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"h.xyz = -h.xyz; return s_translate(h);\n"
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"}\n";
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use_christoffel = false;
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}
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else if(stretch::in()) {
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fsh += "mediump mat4 s_translate(vec4 h) {\n"
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"return mat4(h.w,h.z,-h.y,-h.x,-h.z,h.w,h.x,-h.y,h.y,-h.x,h.w,-h.z,h.x,h.y,h.z,h.w);\n"
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"}\n";
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fsh += "mediump mat4 s_itranslate(vec4 h) {\n"
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"h.xyz = -h.xyz; return s_translate(h);\n"
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"}\n";
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use_christoffel = false;
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if(stretch::mstretch) {
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fsh += "mediump vec4 christoffel(mediump vec4 pos, mediump vec4 vel, mediump vec4 tra) {\n"
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"vel = s_itranslate(pos) * vel;\n"
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"tra = s_itranslate(pos) * tra;\n"
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"return s_translate(pos) * vec4(\n";
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for(int i=0; i<3; i++) {
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auto &c = stretch::ms_christoffel;
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fsh += " 0.";
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for(int j=0; j<3; j++)
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for(int k=0; k<3; k++)
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if(c[i][j][k])
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fsh += " + vel["+its(j)+"]*tra["+its(k)+"]*" + to_glsl(c[i][j][k]);
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fsh += " ,\n";
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}
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fsh += " 0);\n"
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"}\n";
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}
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else
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use_christoffel = false;
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}
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else use_christoffel = false;
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@ -605,7 +635,7 @@ void enable_raycaster() {
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fmain +=
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" dist = next < minstep ? 2.*next : next;\n";
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if(nil) fsh +=
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if(nil && !use_christoffel) fsh +=
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"mediump vec4 translate(mediump vec4 a, mediump vec4 b) {\n"
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"return vec4(a[0] + b[0], a[1] + b[1], a[2] + b[2] + a[0] * b[1], b[3]);\n"
|
||||
"}\n"
|
||||
@ -619,7 +649,7 @@ void enable_raycaster() {
|
||||
"return vec4(t[0], t[1], t[2] - a[0] * t[1], 0.);\n"
|
||||
"}\n";
|
||||
|
||||
if(nil) fmain += "tangent = translate(position, itranslate(position, tangent));\n";
|
||||
// if(nil) fmain += "tangent = translate(position, itranslate(position, tangent));\n";
|
||||
|
||||
if(use_christoffel) fmain +=
|
||||
"mediump vec4 vel = tangent * dist;\n"
|
||||
@ -628,15 +658,24 @@ void enable_raycaster() {
|
||||
"mediump vec4 acc3 = get_acc(position + vel / 2. + acc1/4., vel + acc2/2.);\n"
|
||||
"mediump vec4 acc4 = get_acc(position + vel + acc2/2., vel + acc3/2.);\n"
|
||||
"mediump vec4 nposition = position + vel + (acc1+acc2+acc3)/6.;\n";
|
||||
|
||||
if((sl2 || stretch::in()) && use_christoffel) {
|
||||
if(sl2) fmain +=
|
||||
"nposition = nposition / sqrt(dot(position.zw, position.zw) - dot(nposition.xy, nposition.xy));\n";
|
||||
|
||||
else if(stretch::in()) fmain +=
|
||||
"nposition = nposition / sqrt(dot(nposition, nposition));\n";
|
||||
}
|
||||
|
||||
if(sl2 || stretch::in()) {
|
||||
if((sl2 || stretch::in()) && !use_christoffel) {
|
||||
ld SV = stretch::not_squared();
|
||||
ld mul = (sphere?1:-1)-1/SV/SV;
|
||||
fmain +=
|
||||
"vec4 vel = s_itranslate(position) * tangent * dist;\n"
|
||||
"mediump float vlen = length(vel.xyz);\n"
|
||||
"vec4 vel1 = vel; vel1.z *= " + to_glsl(stretch::not_squared()) + ";\n"
|
||||
"mediump float vlen = length(vel1.xyz);\n"
|
||||
"if(vel.z<0.) vlen=-vlen;\n"
|
||||
"float z_part = vel.z/vlen;\n"
|
||||
"float z_part = vel1.z/vlen;\n"
|
||||
"float x_part = sqrt(1.-z_part*z_part);\n"
|
||||
"const float SV = " + to_glsl(SV) + ";\n"
|
||||
"float rparam = x_part / z_part / SV;\n"
|
||||
@ -718,13 +757,12 @@ void enable_raycaster() {
|
||||
"}\n";
|
||||
|
||||
fmain +=
|
||||
"ntangent = s_itranslate(nposition) * ntangent / dist;\n"
|
||||
"ntangent.z *= SV;\n"
|
||||
"nposition = s_translate(position) * nposition;\n"
|
||||
"ntangent = s_translate(nposition) * ntangent;\n";
|
||||
"ntangent = ntangent / dist;\n"
|
||||
"ntangent = s_translate(position) * ntangent;\n"
|
||||
"nposition = s_translate(position) * nposition;\n";
|
||||
}
|
||||
|
||||
if(nil) {
|
||||
if(nil && !use_christoffel) {
|
||||
fmain +=
|
||||
"mediump vec4 xp, xt;\n"
|
||||
"mediump vec4 back = itranslatev(position, tangent);\n"
|
||||
@ -876,15 +914,31 @@ void enable_raycaster() {
|
||||
"next = maxstep;\n"
|
||||
"}\n";
|
||||
|
||||
fmain +=
|
||||
"position = nposition;\n";
|
||||
|
||||
if(use_christoffel) fmain +=
|
||||
"tangent = tangent + (acc1+2.*acc2+2.*acc3+acc4)/(6.*dist);\n";
|
||||
else if(nil) fmain +=
|
||||
"tangent = translatev(position, xt);\n";
|
||||
else fmain +=
|
||||
"tangent = ntangent;\n";
|
||||
|
||||
fmain +=
|
||||
"position = nposition;\n";
|
||||
|
||||
if((stretch::in() || sl2) && use_christoffel) {
|
||||
fmain +=
|
||||
"tangent = s_itranslate(position) * tangent;\n"
|
||||
"tangent[3] = 0.;\n";
|
||||
if(stretch::mstretch)
|
||||
fmain +=
|
||||
"float nvelsquared = dot(tangent.xyz, (uATOI * tangent).xyz);\n";
|
||||
else
|
||||
fmain +=
|
||||
"float nvelsquared = tangent.x * tangent.x + tangent.y * tangent.y + "
|
||||
+ to_glsl(stretch::squared()) + " * tangent.z * tangent.z;\n";
|
||||
fmain +=
|
||||
"tangent /= sqrt(nvelsquared);\n"
|
||||
"tangent = s_translate(position) * tangent;\n";
|
||||
}
|
||||
}
|
||||
else fmain +=
|
||||
"position = position + tangent * dist;\n";
|
||||
@ -1270,6 +1324,11 @@ EX void cast() {
|
||||
glUniform1f(o->uIPD, vid.ipd);
|
||||
GLERR("uniform mediump IPD");
|
||||
|
||||
if(o->uITOA != -1) {
|
||||
glUniformMatrix4fv(o->uITOA, 1, 0, glhr::tmtogl_transpose3(stretch::m_itoa).as_array());
|
||||
glUniformMatrix4fv(o->uATOI, 1, 0, glhr::tmtogl_transpose3(stretch::m_atoi).as_array());
|
||||
}
|
||||
|
||||
if(o->uWallOffset != -1) {
|
||||
glUniform1i(o->uWallOffset, wall_offset(cs));
|
||||
glUniform1i(o->uSides, cs->type + (WDIM == 2 ? 2 : 0));
|
||||
|
||||
Loading…
Reference in New Issue
Block a user