mirror of
https://github.com/zenorogue/hyperrogue.git
synced 2024-12-29 19:40:35 +00:00
356 lines
13 KiB
C++
356 lines
13 KiB
C++
namespace reps {
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TD typename D::Number acos_auto(typename D::Number x) {
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using N = typename D::Number;
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if(hyperbolic) {
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if(x < N(1)) return N(0);
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return acosh(x);
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}
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if(sphere) {
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if(x > N(1)) return N(0);
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return acos(x);
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}
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throw hr::hr_exception("error");
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}
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/* use the linear representation, as in HyperRogue, but DO NOT apply nm, for comparison */
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TD struct rep_linear_nn {
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using data = D;
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using point = mvector<data>;
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using isometry = matrix<data>;
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using N = typename D::Number;
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static constexpr isometry id() {
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matrix<D> result;
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for(int i=0; i<D::Dim; i++)
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for(int j=0; j<D::Dim; j++)
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result[i][j] = N(i == j);
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return result;
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};
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static constexpr isometry cspin(int i, int j, typename D::Number angle) {
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auto res = id();
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auto ca = cos(angle), sa = sin(angle);
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res[i][i] = ca;
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res[j][j] = ca;
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res[i][j] = sa;
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res[j][i] = -sa;
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return res;
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};
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static constexpr isometry cspin90(int i, int j) {
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auto res = id();
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res[i][i] = 0;
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res[j][j] = 0;
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res[i][j] = 1;
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res[j][i] = -1;
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return res;
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};
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static constexpr isometry lorentz(int i, int j, typename D::Number angle) {
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auto res = id();
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auto ca = cosh(angle), sa = sinh(angle);
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res[i][i] = ca;
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res[j][j] = ca;
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res[i][j] = sa;
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res[j][i] = sa;
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return res;
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}
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static constexpr point center() { return unit_vector<data>(D::Dim-1); }
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static point apply(const isometry& T, const point& x) { return T * x; };
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static isometry apply(const isometry& T, const isometry& U) { return T * U; };
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static typename D::Number dist0(point x) {
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return acos_auto<D> (x[D::Dim-1]);
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}
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static typename D::Number angle(const point& x) { return atan2(x[1], x[0]); }
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static typename D::Number get_coord(point x, int i) { return x[i]; }
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static isometry inverse(isometry T) {
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for(int i=0; i<D::Dim; i++)
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for(int j=0; j<i; j++) std::swap(T[i][j], T[j][i]);
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if constexpr(D::Flipped != -1) {
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for(int i=0; i<D::Dim-1; i++) T[i][D::Dim-1] = -T[i][D::Dim-1];
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for(int i=0; i<D::Dim-1; i++) T[D::Dim-1][i] = -T[D::Dim-1][i];
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}
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return T;
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}
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static isometry push(const point& p) {
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auto res = id();
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// to do: for spherical!
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N fac = N(1)/(p[D::Dim-1]+N(1));
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for(int i=0; i<D::Dim-1; i++)
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for(int j=0; j<D::Dim-1; j++)
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res[i][j] += p[i] * p[j] * fac;
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for(int d=0; d<D::Dim-1; d++)
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res[d][D::Dim-1] = p[d],
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res[D::Dim-1][d] = p[d];
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res[D::Dim-1][D::Dim-1] = p[D::Dim-1];
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return res;
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}
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static std::string print(point p) { return nzv(p); }
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static std::string print(isometry p) { return nzv(p); }
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};
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TD mvector<D> get_column(matrix<D> a, int id) {
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mvector<D> tmp;
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for(int i=0; i<D::Dim; i++) tmp[i] = a[i][id];
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return tmp;
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}
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TD typename D::Number inner(mvector<D> a, mvector<D> b) {
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using N = typename D::Number;
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N res(0);
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for(int i=0; i<D::Dim; i++) res += a[i] * b[i] * (i==D::Flipped?-1:1);
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if(isnan(res) || isinf(res)) return N(0);
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return res;
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}
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TD void set_column(matrix<D>& a, int id, mvector<D> v) {
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for(int i=0; i<D::Dim; i++) a[i][id] = v[i];
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}
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TD typename D::Number sqnorm(matrix<D> a) { return sqnorm<D>(get_column<D>(a, D::Dim-1)); }
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bool fix_matrices;
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TD matrix<D> apply_nm(matrix<D> a) {
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using N = typename D::Number;
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// normalize first
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auto& lead = a[D::Dim-1][D::Dim-1];
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if(nm == nmFlatten) a = a / lead, cbc[cbcDiv]--;
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if(nm == nmForced || nm == nmWeak) a = a * pow(sqnorm<D>(a), -0.5);
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if(nm == nmBinary) {
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while(lead >= 2 && !isinf(lead)) { a = a / 2; } while(lead > 0 && lead < 0.5) { a = a * 2; }
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}
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// fixmatrix later
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if(!fix_matrices) return a;
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auto divby = (nm == nmBinary || nm == nmWeak || nm == nmCareless || nm == nmFlatten) ? sqnorm<D>(a) : N(1);
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for(int i=D::Dim-2; i>=0; i--) {
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auto ro = get_column(a, i);
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auto last = get_column(a, D::Dim-1);
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ro = ro + last * inner(ro, last) / divby;
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for(int j=i+1; j<D::Dim-1; j++) {
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auto next = get_column(a, j);
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ro = ro - next * inner(ro, next) / divby;
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}
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auto in = inner(ro, ro);
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if(in > N(0)) ro = ro * (pow(in*in, -.5) * divby);
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set_column(a, i, ro);
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}
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return a;
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}
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/* use the linear representation, as in HyperRogue */
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TD struct rep_linear {
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using data = D;
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using point = mvector<data>;
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using isometry = matrix<data>;
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using N = typename D::Number;
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static constexpr isometry cspin(int i, int j, typename D::Number angle) {
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return apply_nm<D>( rep_linear_nn<D>::cspin(i, j, angle) );
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}
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static constexpr isometry cspin90(int i, int j) {
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return rep_linear_nn<D>::cspin90(i, j);
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}
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static constexpr isometry lorentz(int i, int j, typename D::Number angle) {
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return apply_nm<D>( rep_linear_nn<D>::lorentz(i, j, angle) );
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}
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static isometry id() { return rep_linear_nn<D>::id(); };
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static constexpr point center() { return unit_vector<data>(D::Dim-1); }
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static point apply(const isometry& T, const point& x) { return apply_nm(T * x); };
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static isometry apply(const isometry& T, const isometry& U) { return apply_nm(T * U); };
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static typename D::Number dist0(point x) {
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return acos_auto<D> (get_normalized(x, x[D::Dim-1]));
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}
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static typename D::Number angle(const point& x) { return atan2(x[1], x[0]); }
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static typename D::Number get_coord(point x, int i) {
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return get_normalized(x, x[i]); }
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static isometry inverse(isometry T) {
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return rep_linear_nn<D>::inverse(T);
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}
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static isometry push(const point& p) {
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return apply_nm( rep_linear_nn<D>::push(get_normalized(p, p)) );
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}
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static std::string print(point p) { return nzv(p); }
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static std::string print(isometry p) { return nzv(p); }
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};
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/* use the linear representation of points and the multivector representation of isometries */
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TD struct rep_mixed {
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using data = D;
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using N = typename D::Number;
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using point = mvector<data>;
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using isometry = multivector<data>;
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static isometry cspin(int i, int j, typename data::Number alpha, bool noflat = false) {
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/* auto u = unit_vector<multivector_data<data>> (0);
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auto ui = unit_vector<data> (i);
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auto uj = unit_vector<data> (j);
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return u * cos(alpha/2) + multimul(embed(ui), embed(uj)) * sin(alpha/2); */
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auto res = zero_vector<multivector_data<data>> ();
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if(nm == nmFlatten && !noflat) {
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res[0] = N(1);
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res[(1<<i) | (1<<j)] = tan(alpha/2) * (i > j ? 1 : -1);
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return res;
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}
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res[0] = cos(alpha/2);
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res[(1<<i) | (1<<j)] = sin(alpha/2) * (i > j ? 1 : -1);
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return res;
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}
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static isometry cspin90(int i, int j, bool noflat = false) {
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auto res = zero_vector<multivector_data<data>> ();
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if(nm == nmFlatten && !noflat) {
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res[0] = N(1);
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res[(1<<i) | (1<<j)] = N(i > j ? 1 : -1);
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return res;
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}
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res[0] = sqrt(N(.5));
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res[(1<<i) | (1<<j)] = sqrt(N(.5)) * (i > j ? 1 : -1);
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return res;
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}
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static isometry lorentz(int i, int j, typename data::Number alpha) {
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/* // j must be time coordinate
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auto u = unit_vector<multivector_data<data>> (0);
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auto ui = unit_vector<data> (i);
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auto uj = unit_vector<data> (j);
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return u * cosh(alpha/2) + multimul(embed(uj), embed(ui)) * sinh(alpha/2); */
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auto res = zero_vector<multivector_data<data>> ();
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if(nm == nmFlatten) {
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res[0] = N(1);
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res[(1<<i) | (1<<j)] = tanh(alpha/2);
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return res;
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}
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res[0] = cosh(alpha/2);
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res[(1<<i) | (1<<j)] = sinh(alpha/2);
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return res;
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}
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static isometry id() { return unit_vector<multivector_data<data>> (0); };
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static constexpr point center() { return unit_vector<data>(D::Dim-1); }
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static point apply(const isometry& T, const point& x) {
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// return unembed(multimul(multimul(T, embed(x)), conjugate(T)));
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return apply_nm(unembed(chkmul<odd<D>,flat_even<D>,underling<D>>(chkmul<flat_even<D>,flat_underling<D>,odd<D>>(T, embed(x)), conjugate(T))));
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};
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static isometry apply(const isometry& T, const isometry& U) {
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auto res = apply_nm<even<D>, D>(chkmul<flat_even<D>,flat_even<D>,even<D>>(T, U));
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return res;
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}
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static isometry inverse(isometry T) { return conjugate(T); }
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static isometry push(const point& p) {
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auto pm = get_normalized(p, p);
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pm[D::Dim-1] = pm[D::Dim-1] + N(1);
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// since p was normalized, sqnorm of pm is 2 * pm[D::Dim-1]
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pm = pm * pow(2 * pm[D::Dim-1], -0.5);
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multivector<data> v1 = embed(pm);
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multivector<data> v2 = unit_vector<multivector_data<data>>(1<<(D::Dim-1));
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multivector<data> v3 = chkmul<underling<D>,underling<D>,poincare<D>>(v1, v2);
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v3 = apply_nm<poincare<D>, D>(v3);
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return v3;
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}
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static typename D::Number dist0(point x) { return acos_auto<D> (get_normalized(x, x[D::Dim-1])); }
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static typename D::Number angle(const point& x) { return atan2(x[1], x[0]); }
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static typename D::Number get_coord(point x, int i) { return get_normalized(x, x[i]); }
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static std::string print(point p) { return nzv(p); }
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static std::string print(isometry p) { return nz(p); }
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};
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/* use the hyperboloid-Poincare representation of points and the multivector representation of isometries */
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TD struct rep_clifford {
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using data = D;
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using N = typename D::Number;
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using point = array< multivector<data>, 1>;
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using isometry = multivector<data>;
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static isometry cspin(int i, int j, typename data::Number alpha) { return rep_mixed<D>::cspin(i, j, alpha); }
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static isometry cspin90(int i, int j) { return rep_mixed<D>::cspin90(i, j); }
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// j must be the neg coordinate!
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static isometry lorentz(int i, int j, N alpha) { return rep_mixed<D>::lorentz(i, j, alpha); }
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static isometry id() { return rep_mixed<D>::id(); }
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static constexpr point center() { return point{{ id() }}; }
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static point apply(const isometry& T, const point& x) { return point{{ despin(chkmul<even<D>,poincare<D>,even<D>>(T, x[0])) }}; }
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static isometry apply(const isometry& T, const isometry& U) { return apply_nm<even<D>,D>( chkmul<even<D>,even<D>,even<D>>(T, U) ); }
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static isometry inverse(isometry T) { return conjugate(T); }
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static isometry push(const point& p) { return p[0]; }
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static typename D::Number dist0(const point& ax) {
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return acos_auto<D>(get_normalized<poincare<D>, D, N>(ax[0], ax[0][0]))*2;
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}
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static constexpr int mvlast = 1<<(D::Dim-1);
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static typename D::Number angle(const point& x) {
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return atan2(x[0][2 | mvlast], x[0][1 | mvlast]);
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}
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static typename D::Number get_coord(const point& x, int i) {
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auto x1 = multimul(multimul(x[0], unit_vector<multivector_data<data>> (mvlast)), conjugate(x[0]));
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auto x2 = unembed(x1);
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return get_normalized(x2, x2[i]);
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}
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static std::string print(point p) { return nz(p[0]); }
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static std::string print(isometry p) { return nz(p); }
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};
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/* split isometries into the poincare and rotational part */
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TD struct rep_gyro {
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using data = D;
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using N = typename D::Number;
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using point = multivector<data>;
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using isometry = poincare_rotation<data>;
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static isometry cspin(int i, int j, typename data::Number alpha) { return { rep_mixed<D>::id(), rep_mixed<D>::cspin(i, j, alpha, true) }; }
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static isometry cspin90(int i, int j, typename data::Number alpha) { return { rep_mixed<D>::id(), rep_mixed<D>::cspin90(i, j, alpha, true) }; }
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static isometry lorentz(int i, int j, typename data::Number alpha) { return {rep_mixed<D>::lorentz(i, j, alpha), rep_mixed<D>::id() }; }
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static isometry id() { return { rep_mixed<D>::id(), rep_mixed<D>::id() }; }
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static constexpr point center() { return rep_mixed<D>::id(); }
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static point apply(const isometry& T, const point& x) { return despin(chkmul<poincare<D>,poincare<D>,even<D>>(T.first, chkmul<rotational<D>,poincare<D>,poincare<D>>(T.second, x))); }
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static isometry apply(const isometry& T, const isometry& U) {
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auto R1 = apply_nm<rotational<D>, poincare<D>, poincare<D>> (T.second, U.first);
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auto R2 = apply_nm<poincare<D>, poincare<D>, even<D>> (T.first, R1);
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auto R3 = despin2(R2);
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return { R3.first, apply_nm<rotational<D>, rotational<D>, rotational<D>> (R3.second, U.second) };
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}
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static isometry inverse(isometry T) { return { conjugate(T.first), conjugate(T.second) }; }
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static isometry push(const point& p) { return { p, rep_mixed<D>::id() }; }
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static typename D::Number dist0(const point& ax) {
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return acos_auto<D>(get_normalized<poincare<D>, D, N>(ax, ax[0]))*2;
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}
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static constexpr int mvlast = 1<<(D::Dim-1);
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static typename D::Number angle(const point& x) {
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return atan2(x[0][2 | mvlast], x[0][1 | mvlast]);
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}
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static typename D::Number get_coord(const point& x, int i) {
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auto x1 = multimul(multimul(x[0], unit_vector<multivector_data<data>> (mvlast)), conjugate(x[0]));
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auto x2 = unembed(x1);
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return get_normalized(x2, x2[i]);
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}
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static std::string print(point p) { return nz(p[0]); }
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static std::string print(isometry p) { return "["+nz(p.first)+","+nz(p.second)+"]"; }
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};
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}
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