Added tests of different operations in general-purpose tables (much like Cayley, but with a general binary function parameter)

Author: jep-dev

app/dual.cpp

@@ -2,6 +2,7 @@
 #include <iostream>
 #include <iomanip>
 #include <vector>
+#include <map>
 
 #ifdef DUAL2
 #include "dual2.hpp"
@@ -15,16 +16,164 @@
 #define DUAL_IMPL "unknown"
 #endif
 
+#include "streams.tpp"
+#include "utility.hpp"
+
+template<class T, unsigned N, unsigned M>
+std::vector<std::string> get_table(std::string const& title,
+		const T (&LHS)[N], const T (&RHS)[M], T (*fn)(T const&, T const&)) {
+	using namespace std;
+	using Streams::center;
+
+	vector<string> out;
+	ostringstream os;
+	char b_n = '-', b_ne = '.', b_e = '|', b_se = '\'',
+			b_s = '-', b_sw = '\'', b_w = '|', b_nw = '.',
+			b_c = '+', b_none = ' ';
+	string utitle = "(u)", vtitle = "(v)", pad = " ";
+	long wu = utitle.length(), wv = vtitle.length(), wtitle = title.length(),
+			rwv = (wv-1)/2, lwv = wv-1-rwv, wcell = max(3l, wu),
+			wpad = pad.length(), wpcell = wcell + wpad * 2, wrow = wpcell * M,
+			dtitle = wtitle + 2;
+	string lv = string(lwv, ' '), rv = string(rwv, ' '),
+			north = b_none + string(wpcell + lwv, ' ') + b_nw
+				+ center(center(title, dtitle, ' '), wrow + rwv, '-') + b_ne,
+		middle = b_nw + center(utitle, wpcell+lwv, '-', false) + b_c + string(wrow+rwv, '-') + b_c,
+		bottom = b_sw + string(wpcell+lwv, '-') + b_c + string(wrow+rwv, '-') + b_se;
+	out.emplace_back(north);
+	string header = b_none + string(wpcell, ' ') + vtitle;
+	for(auto const& rhs : RHS)
+		header += pad + center(rhs, wcell, ' ') + pad;
+	header += b_e;
+	out.emplace_back(header);
+	out.emplace_back(middle);
+	for(auto const& lhs : LHS) {
+		string str = b_w + center(string(lhs), wpcell+lwv, ' ') + b_w + string(rwv, ' ');
+		for(auto const& rhs : RHS) {
+			str += pad + center(fn(lhs, rhs), wcell, ' ', false) + pad;
+		}
+		str += b_e;
+		out.emplace_back(str);
+	}
+	out.emplace_back(bottom);
+	return out;
+}
+
 int main(int argc, const char *argv[]) {
 	using namespace std;
+	using Streams::center;
+
+	cout << "Using dual quaternions as implemented in " << DUAL_IMPL << '.' << endl;
 
 	typedef float T;
 	typedef DualQuaternion<T> DQ;
+	typedef DQ (binary) (DQ const&, DQ const&);
+
+	/*DQ p1 = 1_e + 1_I, p2 = 1_e + 1_J, dp = p2 - p1;
+	// Line: p1 + dp * t
+	DQ x = 1_e + 1_I + 1_J + 1_k, dxp = x - p1,
+		projection = p1 + dp * dot(dxp, dp),
+		rejection = dxp - projection;
+	cout << "Line l from " << p1 << " to " << p2 << " is given by l(t) = "
+			<< p1 << " + (" << dp << ")t" << endl;
+	cout << "Point x = " << x << " is " << dxp << " from " << p1 << endl;
+	cout << "  Projection = " << projection << "\n"
+			"  Rejection = " << rejection << endl;
+
+	return 0;*/
 
-	cout << "Using " << DUAL_IMPL << " to implement dual quaternions!\n" << endl;
+	DQ LHS[] = {1_e, 1_i, 1_j, 1_k, 1_E, 1_I, 1_J, 1_K},
+		RHS[] = {1_i, 1_i + 1_J /* (1_i + 1_j)*T(sqrtf(2)/2) */ };
 
-	DQ LHS[] = {{1}, {0,1}, {0,0,1}, {0,0,0,1},
-			{0,0,0,0,1}, {0,0,0,0,0,1}, {0,0,0,0,0,0,1}, {0,0,0,0,0,0,0,1}};
+	map<string, binary*> functions = {
+		{"W(u, v) = uv", [] (DQ const& l, DQ const& r) -> DQ { return l * r; }},
+		{"W(u, v) = u v *u", [] (DQ const& l, DQ const& r) -> DQ { return l ^ r; }},
+		{"W(u, v) = v u *v", [] (DQ const& l, DQ const& r) -> DQ { return r ^ l; }}
+	};
+	/*auto ntables = functions.size();
+	vector<ostringstream> oss;
+	vector<istringstream> iss;
+	for(auto i = 0; i < ntables; i++) {
+		oss.emplace_back();
+		print_table(oss[i], LHS, LHS, functions[i]);
+		iss.emplace_back(oss[i].str());
+	}*/
+
+	cout << "Sandwich operators: " << endl;
+	vector<vector<std::string>> lines;
+	for(auto const& fn : functions)
+		lines.emplace_back(get_table(fn.first, LHS, LHS, fn.second));
+	for(long k = 0, dk = 2, n = lines.size(); k < n; k += dk) {
+		for(long j = 0, m = lines[0].size(); j < m; j++) {
+			for(long i = k; i < k+dk && i < n; i++) {
+				cout << lines[i][j] << "  ";
+			}
+			cout << endl;
+		}
+	}
+		/*string line;
+		bool cont = true;
+		for(unsigned i = 0; i < ntables; i++) {
+			if(i) cout << "  ";
+			if(!std::getline(iss[i], line)) {
+				cont = false;
+				break;
+			}
+			cout << line;
+		}
+		cout << endl;
+		if(!cont) break;
+	}*/
+
+/*std::vector<std::vector<std::string>> cols = {
+	{"u"}, {"v"}, {"uv"}, {"uvu*"},
+	{"v"}, {"u"}, {"vu"}, {"vuv*"}
+};
+for(auto const& lhs : LHS) {
+	for(auto const& rhs : LHS) {
+		cols[0].emplace_back(to_string(lhs, 3));
+		cols[1].emplace_back(to_string(rhs, 3));
+		cols[2].emplace_back(to_string(rhs * lhs, 3));
+		cols[3].emplace_back(to_string(lhs ^ rhs, 3));
+		cols[4].emplace_back(to_string(rhs, 3));
+		cols[5].emplace_back(to_string(lhs, 3));
+		cols[6].emplace_back(to_string(lhs * rhs, 3));
+		cols[7].emplace_back(to_string(rhs ^ lhs, 3));
+	}
+}
+std::vector<long> maxes;
+for(long j = 0, m = cols.size(); j < m; j++)
+	maxes.emplace_back(minimax(cols[j]).second);
+for(long i = 0, n = cols[0].size(); i < n; i++) {
+	for(long j = 0, m = cols.size(); j < m; j++) {
+		cout << Streams::center(cols[j][i], maxes[j]);
+		if(j == 3) cout << "##";
+		else cout << "   ";
+	}
+	if(!i) {
+		cout << " |  ";
+		for(long j = 0, m = cols.size(); j < m; j++)
+			cout << Streams::center(cols[j][i], maxes[j]) << "   ";
+	}
+	long k = i-1;
+	if(k & 1) endl(cout);
+	//if(i && !(i&1)) endl(cout);
+	else cout << " |  ";
+}*/
+
+	/*cout << setw(3) << "" << " | ";
+	for(auto const& rhs : LHS)
+		cout << setw(3) << rhs << " ";
+	cout << endl;
+	for(auto const& lhs : LHS) {
+		cout << setw(3) << lhs << " | ";
+		for(auto const& rhs : LHS) {
+			cout << setw(3) << (lhs ^ rhs) << " ";
+		}
+		cout << endl;
+	}*/
+	/*DQ LHS[] = {{1}, {0,1}, {0,0,1}, {0,0,0,1},
+			{0,0,0,0,1}, {0,0,0,0,0,1}, {0,0,0,0,0,0,1}, {0,0,0,0,0,0,0,1}};*/
 	for(auto const& lhs : LHS) {
 		for(auto const& rhs : LHS) {
 			cout << setw(3) << (lhs * rhs) << " ";