/**************************** * DrawFunction.js * * This uses the Peter Jipsen's ASCIIsvg.js 1.0. * ASCIIsvg.js is freely available under the GNU General Public License * * Revison: 12 * Resource: limit.ssu.ac.kr/ascii/DrawFunction.js * License: GNU General Public License * Author: Pilho Kim at Soongsil University, phkim (AT) ssu.ac.kr */ var pi = Math.PI var e = Math.E function changeMult(s) { var re = new RegExp("(([0-9|\\)|\\]|!])([a-z|A-Z|\\(|\\[])|([0-9|a-z|A-Z|\\)|\\]|!]+\\s+)" + "([0-9|a-z|A-Z|\\(|\\[]+)" + ")", "gi"); var s1 = s.replace(re, function($0, $1, $2, $3, $4, $5) { var a, b a = ($2 == undefined) ? $4 : $2 b = ($3 == undefined) ? $5 : $3 return a + "*" + b; }); while (s1 != s) return changeMult(s1) return s1 } function changePower(s) { var re = new RegExp("(\\(" + "([^\|]+)" + "\\)|(\\w+\\s*))" + "(\\^|\\*\\*)(\\(" + "([^\|]+)" + "\\)|(\\s*\\w+))", "gi"); return s.replace(re, function($0, $1, $2, $3, $4, $5) { var a, b a = ($2 == undefined) ? $1 : $2 b = ($5 == undefined) ? $4 : $5 return "pow(" + a + "," + b + ")"; }); } function changeFact(s) { var re = new RegExp("(\\(" + "([^\|]+)" + "\\)|(\\w+\\s*))" + "!"); return s.replace(re, function($0, $1, $2) { var a a = ($2 == undefined) ? $1 : $2 return "fact(" + a + ")" }); } function changeLog(s) { var re = new RegExp("log([^a-zA-Z])", "gi"); return s.replace(re, function($0, $1) { if ($1 != undefined) return "Log" + $1 }); } function changeXtoT(s) { var re = new RegExp("x([^a-zA-Z])|([^a-zA-Z])x|(^x)|(x$)", "gi"); return s.replace(re, function($0, $1, $2, $3, $4) { if ($1 != undefined) return "t" + $1 else if ($2 != undefined) return $2 + "t" else if ($3 != undefined) return "t" else if ($4 != undefined) return "t" }); } function changeYtoT(s) { var re = new RegExp("y([^a-zA-Z])|([^a-zA-Z])y|(^y)|(y$)", "gi"); return s.replace(re, function($0, $1, $2, $3, $4) { if ($1 != undefined) return "t" + $1 else if ($2 != undefined) return $2 + "t" else if ($3 != undefined) return "t" else if ($4 != undefined) return "t" }); } function changeYtoX(s) { var re = new RegExp("y([^a-zA-Z])|([^a-zA-Z])y|(^y)|(y$)", "gi"); return s.replace(re, function($0, $1, $2, $3, $4) { if ($1 != undefined) return "x" + $1 else if ($2 != undefined) return $2 + "x" else if ($3 != undefined) return "x" else if ($4 != undefined) return "x" }); } function changeHyperbolic(s) { var re = new RegExp("(sinh|cosh|tanh|sech|csch|coth|asinh|acosh|atanh|asech|acsch|acoth|sinh\\^\\(-1\\)|cosh\\^\\(-1\\)|tanh\\^\\(-1\\)|sech\\^\\(-1\\)|csch\\^\\(-1\\)|coth\\^\\(-1\\))\\(" + "([^\|,]+)" + "\\)", "gi"); return s.replace(re, function($0, $1, $2) { with(Math) { var param0 = $0.toLowerCase(); ///////////////////////////////////////////////////////////// // (cosh(x))**2 // (cosh(x) )**2 // (cosh(x) )**2 // // alert("$0 = " + $0 + "; $1 = " + $1 + ", $2 = " + $2); var k = findFirstRightMatch($2) var s2, s3 if (k >= 0) { s2 = $2.substring(0, k) s3 = $2.substring(k) } else { s2 = $2 s3 = "" } if (param0.substring(0, 5) == "sinh(") return "((exp(" + s2 + ")-exp(-(" + s2 + ")))/2)" + s3; else if (param0.substring(0, 5) == "cosh(") return "((exp(" + s2 + ")+exp(-(" + s2 + ")))/2)" + s3; else if (param0.substring(0, 5) == "tanh(") return "(1-2/((exp(2*(" + s2 + ")))+1))" + s3; else if (param0.substring(0, 5) == "sech(") return "(2/(exp(" + s2 + ")+exp(-(" + s2 + "))))" + s3; else if (param0.substring(0, 5) == "csch(") return "(2/(exp(" + s2 + ")-exp(-(" + s2 + "))))" + s3; else if (param0.substring(0, 5) == "coth(") return "(1+2/((exp(2*(" + s2 + ")))-1))" + s3; else if (param0.substring(0, 10) == "sinh^(-1)(" || param0.substring(0, 6) == "asinh(") return "ln((" + s2 + ")+sqrt(1+(" + s2 + ")*(" + s2 + ")))" + s3; else if (param0.substring(0, 10) == "cosh^(-1)(" || param0.substring(0, 6) == "acosh(") return "ln((" + s2 + ")+sqrt(-1+(" + s2 + ")*(" + s2 + ")))" + s3; else if (param0.substring(0, 10) == "tanh^(-1)(" || param0.substring(0, 6) == "atanh(") return "(ln((1+(" + s2 + "))/(1-(" + s2 + ")))/2)" + s3; else if (param0.substring(0, 10) == "sech^(-1)(" || param0.substring(0, 6) == "asech(") return "ln(1/(" + s2 + ")+sqrt(-1+1/((" + s2 + ")*(" + s2 + "))))" + s3; else if (param0.substring(0, 10) == "csch^(-1)(" || param0.substring(0, 6) == "acsch(") return "ln(1/(" + s2 + ")+sqrt(+1+1/((" + s2 + ")*(" + s2 + "))))" + s3; else if (param0.substring(0, 10) == "coth^(-1)(" || param0.substring(0, 6) == "acoth(") return "(ln((1+(" + s2 + "))/(-1+(" + s2 + ")))/2)" + s3; else return s; } }); } function changeInverseTrig(s) { var re = new RegExp("(sec|csc|cot|arctan|arcsec|arccsc|arccot|asin|acos|asec|acsc|acot|sin\\^\\(-1\\)|cos\\^\\(-1\\)|tan\\^\\(-1\\)|sec\\^\\(-1\\)|csc\\^\\(-1\\)|cot\\^\\(-1\\))\\(" + "([^\|]+)" + "\\)", "gi"); return s.replace(re, function($0, $1, $2) { with(Math) { var param0 = $0.toLowerCase(); if (param0.substring(0, 9) == "sin^(-1)(" || param0.substring(0, 5) == "asin(") return "arcsin(" + $2 + ")"; else if (param0.substring(0, 9) == "cos^(-1)(" || param0.substring(0, 5) == "acos(") return "arccos(" + $2 + ")"; else if (param0.substring(0, 9) == "tan^(-1)(") return "arctan(" + $2 + ")"; else if (param0.substring(0, 9) == "sec^(-1)(" || param0.substring(0, 5) == "asec(" || param0.substring(0, 7) == "arcsec(") return "arccos(1/(" + $2 + "))"; else if (param0.substring(0, 9) == "csc^(-1)(" || param0.substring(0, 5) == "acsc(" || param0.substring(0, 7) == "arccsc(") return "arcsin(1/(" + $2 + "))"; else if (param0.substring(0, 7) == "arccot(" || param0.substring(0, 9) == "cot^(-1)(" || param0.substring(0, 5) == "acot(") return "arccot(" + $2 + ")"; else if (param0.substring(0, 4) == "sec(") return "(1/cos(" + $2 + "))"; else if (param0.substring(0, 4) == "csc(") return "(1/sin(" + $2 + "))"; else if (param0.substring(0, 4) == "cot(") return "(cos(" + $2 + ")/sin(" + $2 + "))"; else return s; } }); } function changeDelim(s, deli1, deli2, t1, t2) { var re = new RegExp(deli1+ "([^\|]+)" + deli2, "gi"); return s.replace(re, function($0, $1) { return t1 + $1 + t2 }); } function changeEqnDelimeters(s) { var t = changeDelim(s, "\\|", "\\|", "abs(", ")") t = changeDelim(t, "\\[", "\\]", "floor(", ")") return t } function pow(a, x) { var z = 1/x b = eval(a) if ((z == Math.floor(z)) && ((z % 2) == 1) && b < 0) { return -Math.pow(-b, x) } else { return Math.pow(b, x) } } function sqrt(x) { if (x < 0) return undefined else { return Math.sqrt(x) } } function fact(n) { if (n <= 0) return 1 else if (n <= 1) return n var z = n for (var i = n - 1; i > 0; i--) z *= i return z } function perm(n, r) { if (n <= 0 || r > n) return undefined else if (r == 0) return 1 var z = n for (var i = 2; i <= r; i++) z *= n - i + 1 return z } function comb(n, r) { if (n <= 0 || r > n) return undefined else if (r == 0) return 1 var z = n for (var i = 2; i <= r; i++) { z *= n - i + 1 z /= i } return z } function Log(a, x) { if (a <= 0 || a == 1) return undefined if (x <= 0) return undefined return Math.log(x)/Math.log(a) } function ln(x) { if (x <= 0) return undefined return Math.log(x) } function Exp(x) { return Math.exp(x) } function exp(x) { return Math.exp(x) } function sin(x) { return Math.sin(x) } function cos(x) { return Math.cos(x) } function tan(x) { var u = Math.cos(x) if (u != 0) return Math.sin(x)/Math.cos(x) else return undefined } function cot(x) { var u = Math.sin(x) if (u != 0) return Math.cos(x)/Math.sin(x) else return undefined } function arcsin(x) { if (-1 <= x && x <= 1) return Math.asin(x) else return undefined } function arccos(x) { if (x == 1) return 0 else if (x == -1) return Math.PI else if (x >= -1 && x <= 1) return Math.acos(x) else return undefined } function sec(x) { var u = Math.cos(x) if (u != 0) return 1/u else return Number.NaN } function csc(x) { var u = Math.sin(x) if (u != 0) return 1/u else return undefined } function arctan(x) { return Math.atan(x) } function arccot(x) { if (x > 0) return Math.atan(1/x) else if (x < 0) return Math.PI + Math.atan(1/x) else return Math.PI/2 } function sinh(x) { return (Math.exp(x) - Math.exp(-x))/2 } function cosh(x) { return (Math.exp(x) + Math.exp(-x))/2 } function tanh(x) { return (Math.exp(2*x) - 1)/(Math.exp(2*x) + 1) } function sech(x) { return 2/(Math.exp(x) + Math.exp(-x)) } function csch(x) { if (x != 0) return 2/(Math.exp(x) - Math.exp(-x)) else return undefined } function coth(x) { if (x != 0) return (Math.exp(2*x) + 1)/(Math.exp(2*x) - 1) else return undefined } function showStack(arr) { var str = "[" for (var i = 0; i < arr.length; i++) { if (i > 0) str += ", " str += arr[i] } str += "]" } function isWhite(c) { return (c == ' ' || c == '\t' || c == '\f' || c == '\n' || c == '\r') } function isDigit(c) { return (c == "." || (c >= '0' && c <= '9')) } function isComma(c) { return (c == ',') } function isChar(c) { return (c == "_" || (c >= 'a' && c <= 'z') || (c >= 'A' && c <= 'Z')) } function isCharOrDigit(c) { return (isChar(c) || isDigit(c)) } function isLParen(c) { return (c == "(") } function isRParen(c) { return (c == ")") } ////////////////////////////////////////////// // Test Parsing: // 1+(1+2)^(3+(2)-1) // 1+(1+(2))^(3+(2)-1) // 1+(1+(sin(2))^(3+(2)-1)) // 1+4^((-1-(2)))+3 // // 1+(2)^3 // 1+2^3 // 10 -(1+2)^3 // 1+2+2^((-1-(2)))+3 // 1+((2))! // 1+((2)!) // 1+((2))^3 // 1+((2)^3) // // 1+(3!) // 1+(2^3) // 1+(2)^3 // 1+(-2)^3 // 1+2^3 function findFirstRightMatch(s) { var len = s.length var depth = 0 var a var i = 0 for (i = 0; i < len; i++) { a = s.charAt(i) if (isLParen(a)) { depth++ } else if (isRParen(a)) { if (depth <= 0) return i; else depth-- } } return -1 } function changeLeftRightToken(s, op, fnName) { var pos = s.indexOf(op) if (pos < 0) return s; var len = s.length var s1 = s.substring(pos) var s2 = s.substring(pos + 1) var START_STATE = 0 var WHITE_STATE = 1 var COMMA_STATE = 2 var CHAR_STATE = 3 var DIGIT_STATE = 4 var LPAREN_STATE = 5 var RPAREN_STATE = 6 var SYMBOL_STATE = 7 var FINAL_STATE = 99 var state = START_STATE var pos1 = pos, pos2 = pos var hasToken = false var depth = 0 var a var i = 0 for (i = pos + op.length; i < len; i++) { a = s.charAt(i) switch (state) { case START_STATE: if (isWhite(a)) state = WHITE_STATE else if (isDigit(a)) { hasToken = true state = DIGIT_STATE } else if (isChar(a)) { hasToken = true state = CHAR_STATE } else if (isLParen(a)) { depth++ hasToken = true state = LPAREN_STATE } else if (!hasToken && isRParen(a)) { alert("The right parenthesis ')' is in bad position!") return s.substring(0, pos) } else { state = SYMBOL_STATE } break case DIGIT_STATE: case CHAR_STATE: if (isWhite(a)) state = WHITE_STATE else if (isComma(a)) { state = COMMA_STATE } else if (isDigit(a)) { state = DIGIT_STATE } else if (isChar(a)) { state = CHAR_STATE } else if (isLParen(a)) { depth++ state = LPAREN_STATE } else if (isRParen(a)) { if (!hasToken && depth <= 0) { alert("The right parenthesis ')' is in bad position!") return s.substring(0, pos) } depth-- state = RPAREN_STATE } else { state = SYMBOL_STATE } break case LPAREN_STATE: if (isWhite(a)) state = WHITE_STATE else if (isDigit(a)) { state = DIGIT_STATE } else if (isChar(a)) { state = CHAR_STATE } else if (isLParen(a)) { depth++ state = LPAREN_STATE } else if (isRParen(a)) { depth-- state = RPAREN_STATE } else { state = SYMBOL_STATE } break case RPAREN_STATE: if (isWhite(a)) state = WHITE_STATE else if (isDigit(a)) { state = DIGIT_STATE } else if (isChar(a)) { state = CHAR_STATE } else if (isLParen(a)) { depth++ state = LPAREN_STATE } else if (isRParen(a)) { depth-- state = RPAREN_STATE } else { state = SYMBOL_STATE } break case WHITE_STATE: if (isDigit(a)) { hasToken = true state = DIGIT_STATE } else if (isChar(a)) { hasToken = true state = CHAR_STATE } else if (isComma(a)) { hasToken = true state = COMMA_STATE } else if (isLParen(a)) { depth++ hasToken = true state = LPAREN_STATE } else if (isRParen(a)) { if (depth <= 0) { alert("The right parenthesis ')' is in bad position!") return s.substring(0, i+1) } depth-- state = RPAREN_STATE } break case COMMA_STATE: if (isDigit(a)) { hasToken = true state = DIGIT_STATE } else if (isChar(a)) { hasToken = true state = CHAR_STATE } else if (isLParen(a)) { depth++ hasToken = true state = LPAREN_STATE } else if (isRParen(a)) { if (depth <= 0) { alert("The right parenthesis ')' is in bad position!") return s.substring(0, i+1) } depth-- state = RPAREN_STATE } break case SYMBOL_STATE: if (isWhite(a)) { hasToken = true state = WHITE_STATE } else if (isDigit(a)) { hasToken = true state = DIGIT_STATE } else if (isChar(a)) { hasToken = true state = CHAR_STATE } else if (isLParen(a)) { depth++ hasToken = true state = LPAREN_STATE } else if (isRParen(a)) { depth-- state = RPAREN_STATE } break } if (hasToken && depth <= 0 && (state == WHITE_STATE || state == SYMBOL_STATE || state == RPAREN_STATE)) { if (state == RPAREN_STATE) i++ break } } pos2 = i state = START_STATE hasToken = false depth = 0 i = 0 for (i = pos - 1; i >= 0; i--) { a = s.charAt(i) switch (state) { case START_STATE: if (isWhite(a)) state = WHITE_STATE else if (isDigit(a)) { hasToken = true state = DIGIT_STATE } else if (isChar(a)) { hasToken = true state = CHAR_STATE } else if (isComma(a)) { hasToken = true state = COMMA_STATE } else if (!hasToken && isLParen(a)) { alert("The left parenthesis '(' is in bad position!") return s.substring(0, pos) } else if (isRParen(a)) { depth++ hasToken = true state = RPAREN_STATE } else { state = SYMBOL_STATE } break case DIGIT_STATE: case CHAR_STATE: if (isWhite(a)) state = WHITE_STATE else if (isDigit(a)) { state = DIGIT_STATE } else if (isChar(a)) { state = CHAR_STATE } else if (isLParen(a)) { if (!hasToken && depth <= 0) { alert("The left parenthesis '(' is in bad position!") return s.substring(0, pos) } depth-- state = LPAREN_STATE } else if (isRParen(a)) { depth++ state = RPAREN_STATE } else { state = SYMBOL_STATE } break case LPAREN_STATE: if (isWhite(a)) state = WHITE_STATE else if (isDigit(a)) { state = DIGIT_STATE } else if (isChar(a)) { state = CHAR_STATE } else if (isLParen(a)) { depth-- state = LPAREN_STATE } else if (isRParen(a)) { depth++ state = RPAREN_STATE } else { state = SYMBOL_STATE } break case RPAREN_STATE: if (isWhite(a)) state = WHITE_STATE else if (isDigit(a)) { state = DIGIT_STATE } else if (isChar(a)) { state = CHAR_STATE } else if (isLParen(a)) { depth-- state = LPAREN_STATE } else if (isRParen(a)) { depth++ state = RPAREN_STATE } else { state = SYMBOL_STATE } break case WHITE_STATE: if (isDigit(a)) { hasToken = true state = DIGIT_STATE } else if (isChar(a)) { hasToken = true state = CHAR_STATE } else if (isLParen(a)) { depth-- hasToken = true state = LPAREN_STATE } else if (isRParen(a)) { if (!hasToken && depth <= 0) { alert("The right parenthesis ')' is in bad position!") return s.substring(0, i+1) } depth++ state = RPAREN_STATE } break case COMMA_STATE: if (isDigit(a)) { hasToken = true state = DIGIT_STATE } else if (isChar(a)) { hasToken = true state = CHAR_STATE } else if (isLParen(a)) { depth-- hasToken = true state = LPAREN_STATE } else if (isRParen(a)) { if (!hasToken && depth <= 0) { alert("The right parenthesis ')' is in bad position!") return s.substring(0, i+1) } depth++ state = RPAREN_STATE } break case SYMBOL_STATE: if (isWhite(a)) { hasToken = true state = WHITE_STATE } else if (isDigit(a)) { hasToken = true state = DIGIT_STATE } else if (isChar(a)) { hasToken = true state = CHAR_STATE } else if (isLParen(a)) { depth-- state = LPAREN_STATE } else if (isRParen(a)) { depth++ hasToken = true state = RPAREN_STATE } break } if (hasToken && depth <= 0 && (state == WHITE_STATE || state == SYMBOL_STATE || state == LPAREN_STATE)) { if (depth == 0 && state == LPAREN_STATE) i-- break } } pos1 = i var s3 = s.substring(0, pos1 + 1) + fnName + "(" + s.substring(pos1 + 1, pos) + "," + s.substring(pos+op.length, pos2) + ")" + s.substring(pos2) return s3 } ////////////////////////////////////////////// // Test Parsing: // 1+(1+3)! // 1+((1+3)!) // 1+sin((1+3)!) // // 1+(3!) function changeLeftToken(s, op, fnName) { var pos = s.indexOf(op) if (pos < 0) return s; var len = s.length var START_STATE = 0 var WHITE_STATE = 1 var CHAR_STATE = 2 var DIGIT_STATE = 3 var LPAREN_STATE = 4 var RPAREN_STATE = 5 var SYMBOL_STATE = 6 var FINAL_STATE = 99 var state = START_STATE var pos1 = pos var hasToken = false var depth = 0 var a var i = 0 for (i = pos - 1; i >= 0; i--) { a = s.charAt(i) switch (state) { case START_STATE: if (isWhite(a)) state = WHITE_STATE else if (isDigit(a)) { hasToken = true state = DIGIT_STATE } else if (isChar(a)) { hasToken = true state = CHAR_STATE } else if (!hasToken && isLParen(a)) { alert("The left parenthesis '(' is in bad position!") return s.substring(0, i+1) } else if (isRParen(a)) { depth++ hasToken = true state = RPAREN_STATE } else { state = SYMBOL_STATE } break case DIGIT_STATE: case CHAR_STATE: if (isWhite(a)) state = WHITE_STATE else if (isDigit(a)) { state = DIGIT_STATE } else if (isChar(a)) { state = CHAR_STATE } else if (isLParen(a)) { if (!hasToken && depth <= 0) { alert("The left parenthesis '(' is in bad position!") return s.substring(0, i+1) } depth-- state = LPAREN_STATE } else if (isRParen(a)) { depth++ state = RPAREN_STATE } else { state = SYMBOL_STATE } break case LPAREN_STATE: if (isWhite(a)) state = WHITE_STATE else if (isDigit(a)) { state = DIGIT_STATE } else if (isChar(a)) { state = CHAR_STATE } else if (isLParen(a)) { depth-- state = LPAREN_STATE } else if (isRParen(a)) { depth++ state = RPAREN_STATE } else { state = SYMBOL_STATE } break case RPAREN_STATE: if (isWhite(a)) state = WHITE_STATE else if (isDigit(a)) { state = DIGIT_STATE } else if (isChar(a)) { state = CHAR_STATE } else if (isLParen(a)) { depth-- state = LPAREN_STATE } else if (isRParen(a)) { depth++ state = RPAREN_STATE } else { state = SYMBOL_STATE } break case WHITE_STATE: if (isDigit(a)) { hasToken = true state = DIGIT_STATE } else if (isChar(a)) { hasToken = true state = CHAR_STATE } else if (isLParen(a)) { depth-- hasToken = true state = LPAREN_STATE } else if (isRParen(a)) { if (!hasToken && depth <= 0) { alert("The right parenthesis ')' is in bad position!") return s.substring(0, i+1) } depth++ state = RPAREN_STATE } break case SYMBOL_STATE: if (isWhite(a)) { hasToken = true state = WHITE_STATE } else if (isDigit(a)) { hasToken = true state = DIGIT_STATE } else if (isChar(a)) { hasToken = true state = CHAR_STATE } else if (isLParen(a)) { depth-- state = LPAREN_STATE } else if (isRParen(a)) { depth++ hasToken = true state = RPAREN_STATE } break } if (hasToken && depth <= 0 && (state == WHITE_STATE || state == SYMBOL_STATE || state == LPAREN_STATE)) { break } } pos1 = i var s3 = s.substring(0, pos1 + 1) + fnName + "(" + s.substring(pos1 + 1, pos) + ")" + s.substring(pos + op.length) return s3 } function parseEqn(s) { var t = changeXtoT(s) t = changeLog(t) t = changeMult(t); t = changeInverseTrig(t) while (t.indexOf("^") >= 0) { t = changeLeftRightToken(t, "^", "pow") } while (t.indexOf("**") >= 0) { t = changeLeftRightToken(t, "**", "pow") } while (t.indexOf("!") >= 0) { t = changeLeftToken(t, "!", "fact") } t = changeEqnDelimeters(t) t = changeHyperbolic(t) t = t.replace(/\s/gi, "") return t } function evaluateEqn(s) { var value = eval(parseEqn(s)) return value } function drawFunction(figName, s, sx1, sx2, sy1, sy2, color) { var x1, x2, y1, y2 with (Math) { x1 = eval(parseEqn(sx1)) x2 = eval(parseEqn(sx2)) y1 = eval(parseEqn(sy1)) y2 = eval(parseEqn(sy2)) } if (x1 < x2 && y1 < y2) { initPicture(figName, x1, x2, y1, y2) axes() stroke = "silver" text([x2,0],"x","belowleft","x-axis"); text([0, y2],"y","belowleft","y-axis"); text([0, 0],"O","belowleft","origin-mark"); for (var t = 1; less(t, x2); t += 1) { dashline([t, y1], [t, y2], "3 5", ""); text2([t, 0], ""+t, "Arial", "", 12,"below",""); } for (var t = -1; less(x1, t); t -= 1) { dashline([t, y1], [t, y2], "3 5", ""); text2([t, 0],""+t, "Arial", "", 12,"below",""); } for (var t = 1; less(t, y2); t += 1) { dashline([x1, t], [x2, t], "3 5", ""); text2([0, t],""+t, "Arial", "", 12,"left",""); } for (var t = -1; less(y1, t); t -= 1) { dashline([x1, t], [x2, t], "3 5", ""); text2([0, t],""+t, "Arial", "", 12,"left",""); } // marker = "blue" stroke = color var a = [] var sy = parseEqn(s) var y; var delta = (eval(x2) - eval(x1))/200; with (Math) { for (var t = x1; less(t, x2+delta); t += delta) { y = eval(sy); if (y == undefined || y == Number.NaN) { if (a.length > 0) path(a) a = [] continue } else if (a.length > 0 && abs(y - a[a.length - 1][1])/delta > 200 ) { if (a.length > 0) path(a) a = [] continue } else a[a.length] = [t, y] } } path(a) } } function drawManyFunctions(figName, str, sx1, sx2, sy1, sy2) { var colors = ["blue", "green", "red", "navy", "seagreen", "darkgrey", "goldenrod", "magenta"] var x1, x2, y1, y2 with (Math) { x1 = eval(parseEqn(sx1)) x2 = eval(parseEqn(sx2)) y1 = eval(parseEqn(sy1)) y2 = eval(parseEqn(sy2)) } var ss = str.split(";") if (x1 < x2 && y1 < y2) { initPicture(figName, x1, x2, y1, y2) axes() stroke = "silver" text([x2,0],"x","belowleft","x-axis"); text([0, y2],"y","belowleft","y-axis"); text([0, 0],"O","belowleft","origin-mark"); for (var t = 1; less(t, x2); t += 1) { dashline([t, y1], [t, y2], "3 5", ""); text2([t, 0], ""+t, "Arial", "", 12,"below",""); } for (var t = -1; less(x1, t); t -= 1) { dashline([t, y1], [t, y2], "3 5", ""); text2([t, 0],""+t, "Arial", "", 12,"below",""); } for (var t = 1; less(t, y2); t += 1) { dashline([x1, t], [x2, t], "3 5", ""); text2([0, t],""+t, "Arial", "", 12,"left",""); } for (var t = -1; less(y1, t); t -= 1) { dashline([x1, t], [x2, t], "3 5", ""); text2([0, t],""+t, "Arial", "", 12,"left",""); } // marker = "blue" var s var sy var y var delta for (var i = 0; i < ss.length; i++) { s = ss[i] stroke = colors[i % colors.length] sy = parseEqn(s) delta = (eval(x2) - eval(x1))/200; var a = [] with (Math) for (var t = x1; less(t, x2+delta); t += delta) { y = eval(sy); if (y == undefined || y == Number.NaN) { if (a.length > 0) path(a) a = [] continue } else if (a.length > 0 && abs(y - a[a.length - 1][1])/delta > 200 ) { if (a.length > 0) path(a) a = [] continue } else a[a.length] = [t, y] } path(a) } } } function drawFunctionWithAsymptotic(figName, s, asyms, sx1, sx2, sy1, sy2, color) { var x1, x2, y1, y2 with (Math) { x1 = eval(parseEqn(sx1)) x2 = eval(parseEqn(sx2)) y1 = eval(parseEqn(sy1)) y2 = eval(parseEqn(sy2)) } if (x1 < x2 && y1 < y2) { initPicture(figName, x1, x2, y1, y2) axes() stroke = "silver" text([x2,0],"x","belowleft","x-axis"); text([0, y2],"y","belowleft","y-axis"); text([0, 0],"O","belowleft","origin-mark"); for (var t = 1; less(t, x2); t += 1) { dashline([t, y1], [t, y2], "3 5", ""); text2([t, 0], ""+t, "Arial", "", 12,"below",""); } for (var t = -1; less(x1, t); t -= 1) { dashline([t, y1], [t, y2], "3 5", ""); text2([t, 0],""+t, "Arial", "", 12,"below",""); } for (var t = 1; less(t, y2); t += 1) { dashline([x1, t], [x2, t], "3 5", ""); text2([0, t],""+t, "Arial", "", 12,"left",""); } for (var t = -1; less(y1, t); t -= 1) { dashline([x1, t], [x2, t], "3 5", ""); text2([0, t],""+t, "Arial", "", 12,"left",""); } // marker = "blue" var s1 var sy, sx var y, x var delta for (var i = 0; i < asyms.length; i++) { s1 = asyms[i] s1 = s1.replace(/^\s*/,"") stroke = "gray" if (s1.substring(0, 1) == "y" && s1.indexOf("=") > 0) { s1 = s1.substring(s1.indexOf("=") + 1) sy = parseEqn(s1) delta = (x2 - x1)/200; var a = [] with (Math) for (var t = x1; less(t, x2+delta); t += delta) { y = eval(sy); if (y == undefined || y == Number.NaN) { if (a.length > 0) dashpath(a, null, null, "5 5") a = [] continue } else if (a.length > 0 && abs(y - a[a.length - 1][1])/delta > 200 ) { if (a.length > 0) dashpath(a, null, null, "5 5") a = [] continue } else a[a.length] = [t, y] } dashpath(a, null, null, "5 5") } else if (s1.substring(0, 1) == "x" && s1.indexOf("=") > 0) { s1 = s1.substring(s1.indexOf("=") + 1) s1 = s1.replace(/y/g, "x") sx = parseEqn(s1) delta = (y2 - y1)/200; var a = [] with (Math) for (var t = y1; less(t, y2+delta); t += delta) { x = eval(sx); if (x == undefined || x == Number.NaN) { if (a.length > 0) dashpath(a, null, null, "5 5") a = [] continue } else if (a.length > 0 && abs(x - a[a.length - 1][1])/delta > 200 ) { if (a.length > 0) dashpath(a, null, null, "5 5") a = [] continue } else a[a.length] = [x, t] } dashpath(a, null, null, "5 5") } } stroke = color var a = [] sy = parseEqn(s) delta = (eval(x2) - eval(x1))/200; with (Math) { var t for (t = x1; less(t, x2); t += delta) { y = eval(sy); if (y == undefined || y == Number.NaN) { if (a.length > 0) path(a) a = [] continue } else if (a.length > 0 && abs(y - a[a.length - 1][1])/delta > 200 ) { if (a.length > 0) path(a) a = [] continue } else a[a.length] = [t, y] } t = x2 y = eval(sy); if (y == undefined || y == Number.NaN) a[a.length] = [t, y] } path(a) } } function drawFunctionWithAsymptotics(figName, s, asyms, sx1, sx2, sy1, sy2, dx1, dx2, dy1, dy2, color) { var wx1, wx2, wy1, wy2 var x1, x2, y1, y2 with (Math) { wx1 = eval(parseEqn(sx1)) wx2 = eval(parseEqn(sx2)) wy1 = eval(parseEqn(sy1)) wy2 = eval(parseEqn(sy2)) x1 = eval(parseEqn(dx1)) x2 = eval(parseEqn(dx2)) y1 = eval(parseEqn(dy1)) y2 = eval(parseEqn(dy2)) } if (wx1 < wx2 && wy1 < wy2) { initPicture(figName, wx1, wx2, wy1, wy2) axes() stroke = "silver" text([wx2,0],"x","belowleft","x-axis"); text([0, wy2],"y","belowleft","y-axis"); text([0, 0],"O","belowleft","origin-mark"); for (var t = 1; less(t, wx2); t += 1) { dashline([t, wy1], [t, wy2], "3 5", ""); text2([t, 0], ""+t, "Arial", "", 12,"below",""); } for (var t = -1; less(wx1, t); t -= 1) { dashline([t, wy1], [t, wy2], "3 5", ""); text2([t, 0],""+t, "Arial", "", 12,"below",""); } for (var t = 1; less(t, wy2); t += 1) { dashline([wx1, t], [wx2, t], "3 5", ""); text2([0, t],""+t, "Arial", "", 12,"left",""); } for (var t = -1; less(wy1, t); t -= 1) { dashline([wx1, t], [wx2, t], "3 5", ""); text2([0, t],""+t, "Arial", "", 12,"left",""); } // marker = "blue" var s1 var sy, sx var y, x var delta for (var i = 0; i < asyms.length; i++) { s1 = asyms[i] s1 = s1.replace(/^\s*/,"") stroke = "gray" if (s1.substring(0, 1) == "y" && s1.indexOf("=") > 0) { s1 = s1.substring(s1.indexOf("=") + 1) sy = parseEqn(s1) delta = (x2 - x1)/200; var a = [] with (Math) for (var t = x1; less(t, x2+delta); t += delta) { y = eval(sy); if (y == undefined || y == Number.NaN) { if (a.length > 0) dashpath(a, null, null, "5 5") a = [] continue } else if (a.length > 0 && abs(y - a[a.length - 1][1])/delta > 200 ) { if (a.length > 0) dashpath(a, null, null, "5 5") a = [] continue } else a[a.length] = [t, y] } dashpath(a, null, null, "5 5") } else if (s1.substring(0, 1) == "x" && s1.indexOf("=") > 0) { s1 = s1.substring(s1.indexOf("=") + 1) s1 = s1.replace(/y/g, "x") sx = parseEqn(s1) delta = (y2 - y1)/200; var a = [] with (Math) for (var t = y1; less(t, y2+delta); t += delta) { x = eval(sx); if (x == undefined || x == Number.NaN) { if (a.length > 0) dashpath(a, null, null, "5 5") a = [] continue } else if (a.length > 0 && abs(x - a[a.length - 1][1])/delta > 200 ) { if (a.length > 0) dashpath(a, null, null, "5 5") a = [] continue } else a[a.length] = [x, t] } dashpath(a, null, null, "5 5") } } stroke = color var a = [] s = s.replace(/^\s*/,"") if (s.substring(0, 1) == "y" && s.indexOf("=") > 0) { s = s.substring(s.indexOf("=") + 1) sy = parseEqn(s) delta = (eval(x2) - eval(x1))/200; with (Math) { var t for (t = x1; less(t, x2); t += delta) { y = eval(sy) if (y == undefined || y == Number.NaN) { if (a.length > 0) path(a) a = [] continue } else if (a.length > 0 && abs(y - a[a.length - 1][1])/delta > 200 ) { if (a.length > 0) path(a) a = [] continue } else a[a.length] = [t, y] } t = x2 y = eval(sy); if (y == undefined || y == Number.NaN) a[a.length] = [t, y] } path(a) } else if (s.substring(0, 1) == "x" && s.indexOf("=") > 0) { s = s.substring(s.indexOf("=") + 1) s = changeYtoT(s) sy = parseEqn(s) delta = (eval(y2) - eval(y1))/200; with (Math) { var t for (t = y1; less(t, y2); t += delta) { y = eval(sy); if (y == undefined || y == Number.NaN) { if (a.length > 0) path(a) a = [] continue } else if (a.length > 0 && abs(y - a[a.length - 1][0])/delta > 200 ) { if (a.length > 0) path(a) a = [] continue } else a[a.length] = [y, t] } t = y2 y = eval(sy); if (y == undefined || y == Number.NaN) a[a.length] = [y, t] } path(a) } } } function drawParamCurveWithAsymptotics(figName, fnF, fnG, asyms, sx1, sx2, sy1, sy2, dt1, dt2, dx1, dx2, dy1, dy2, color) { var wx1, wx2, wy1, wy2 var t1, t2, x1, x2, y1, y2 with (Math) { wx1 = eval(parseEqn(sx1)) wx2 = eval(parseEqn(sx2)) wy1 = eval(parseEqn(sy1)) wy2 = eval(parseEqn(sy2)) t1 = eval(parseEqn(dt1)) t2 = eval(parseEqn(dt2)) x1 = eval(parseEqn(dx1)) x2 = eval(parseEqn(dx2)) y1 = eval(parseEqn(dy1)) y2 = eval(parseEqn(dy2)) } if (wx1 < wx2 && wy1 < wy2) { initPicture(figName, wx1, wx2, wy1, wy2) axes() stroke = "silver" text([wx2,0],"x","belowleft","x-axis"); text([0, wy2],"y","belowleft","y-axis"); text([0, 0],"O","belowleft","origin-mark"); for (var t = 1; less(t, wx2); t += 1) { dashline([t, wy1], [t, wy2], "3 5", ""); text2([t, 0], ""+t, "Arial", "", 12,"below",""); } for (var t = -1; less(wx1, t); t -= 1) { dashline([t, wy1], [t, wy2], "3 5", ""); text2([t, 0],""+t, "Arial", "", 12,"below",""); } for (var t = 1; less(t, wy2); t += 1) { dashline([wx1, t], [wx2, t], "3 5", ""); text2([0, t],""+t, "Arial", "", 12,"left",""); } for (var t = -1; less(wy1, t); t -= 1) { dashline([wx1, t], [wx2, t], "3 5", ""); text2([0, t],""+t, "Arial", "", 12,"left",""); } // marker = "blue" var s1 var sy, sx var y, x var delta for (var i = 0; i < asyms.length; i++) { s1 = asyms[i] s1 = s1.replace(/^\s*/,"") stroke = "gray" if (s1.substring(0, 1) == "y" && s1.indexOf("=") > 0) { s1 = s1.substring(s1.indexOf("=") + 1) sy = parseEqn(s1) delta = (x2 - x1)/200; var a = [] with (Math) for (var t = x1; less(t, x2+delta); t += delta) { y = eval(sy); if (y == undefined || y == Number.NaN) { if (a.length > 0) dashpath(a, null, null, "5 5") a = [] continue } else if (a.length > 0 && abs(y - a[a.length - 1][1])/delta > 200 ) { if (a.length > 0) dashpath(a, null, null, "5 5") a = [] continue } else a[a.length] = [t, y] } dashpath(a, null, null, "5 5") } else if (s1.substring(0, 1) == "x" && s1.indexOf("=") > 0) { s1 = s1.substring(s1.indexOf("=") + 1) s1 = s1.replace(/y/g, "x") sx = parseEqn(s1) delta = (y2 - y1)/200; var a = [] with (Math) for (var t = y1; less(t, y2+delta); t += delta) { x = eval(sx); if (x == undefined || x == Number.NaN) { if (a.length > 0) dashpath(a, null, null, "5 5") a = [] continue } else if (a.length > 0 && abs(x - a[a.length - 1][1])/delta > 200 ) { if (a.length > 0) dashpath(a, null, null, "5 5") a = [] continue } else a[a.length] = [x, t] } dashpath(a, null, null, "5 5") } } stroke = color var a = [] var sf = fnF.replace(/^\s*/,"") var sg = fnG.replace(/^\s*/,"") var f = parseEqn(sf) var g = parseEqn(sg) delta = (eval(t2) - eval(t1))/200; with (Math) { var t for (t = t1; less(t, t2); t += delta) { x = eval(f) y = eval(g) if (y == undefined || y == Number.NaN || x == undefined || x == Number.NaN) { if (a.length > 0) path(a) a = [] continue } else if (a.length > 0 && abs(y - a[a.length - 1][1])/delta > 200 ) { if (a.length > 0) path(a) a = [] continue } else a[a.length] = [x, y] } t = t2 x = eval(f); y = eval(g); if (y == undefined || y == Number.NaN || x == undefined || x == Number.NaN) a[a.length] = [x, y] } path(a) } } function drawPolarCurveWithAsymptotics(figName, fnF, asyms, sx1, sx2, sy1, sy2, dt1, dt2, dx1, dx2, dy1, dy2, color) { var wx1, wx2, wy1, wy2 var t1, t2, x1, x2, y1, y2 with (Math) { wx1 = eval(parseEqn(sx1)) wx2 = eval(parseEqn(sx2)) wy1 = eval(parseEqn(sy1)) wy2 = eval(parseEqn(sy2)) t1 = eval(parseEqn(dt1)) t2 = eval(parseEqn(dt2)) x1 = eval(parseEqn(dx1)) x2 = eval(parseEqn(dx2)) y1 = eval(parseEqn(dy1)) y2 = eval(parseEqn(dy2)) } if (wx1 < wx2 && wy1 < wy2) { initPicture(figName, wx1, wx2, wy1, wy2) axes() stroke = "silver" text([wx2,0],"x","belowleft","x-axis"); text([0, wy2],"y","belowleft","y-axis"); text([0, 0],"O","belowleft","origin-mark"); with (Math) { for (var t = 0.5; less(t, sqrt(wx2*wx2 + wy2*wy2)); t += 0.5) { dashcircle([0,0], t, "3 5", ""); text2([t, 0], ""+t, "Arial", "", 12,"below",""); text2([-t, 0], ""+(-t), "Arial", "", 12,"below",""); text2([0, t], ""+t, "Arial", "", 12,"left",""); text2([0, -t], ""+(-t), "Arial", "", 12,"left",""); } for (var t = pi/12; less(t, pi/4); t += pi/12) { dashline([0,0], [wx2, tan(t)*wx2], "3 5", ""); dashline([0,0], [wx2, -tan(t)*wx2], "3 5", ""); dashline([0,0], [wx1, tan(t)*wx1], "3 5", ""); dashline([0,0], [wx1, -tan(t)*wx1], "3 5", ""); } for (var t = pi/4; less(t, pi/2); t += pi/12) { dashline([0,0], [cot(t)*wx2, wy2], "3 5", ""); dashline([0,0], [cot(t)*wx2, -wy2], "3 5", ""); dashline([0,0], [cot(t)*wx1, wy1], "3 5", ""); dashline([0,0], [cot(t)*wx1, -wy1], "3 5", ""); } } // marker = "blue" var s1 var sy, sx var y, x var delta for (var i = 0; i < asyms.length; i++) { s1 = asyms[i] s1 = s1.replace(/^\s*/,"") stroke = "gray" if (s1.substring(0, 1) == "y" && s1.indexOf("=") > 0) { s1 = s1.substring(s1.indexOf("=") + 1) sy = parseEqn(s1) delta = (x2 - x1)/200; var a = [] with (Math) for (var t = x1; less(t, x2+delta); t += delta) { y = eval(sy); if (y == undefined || y == Number.NaN) { if (a.length > 0) dashpath(a, null, null, "5 5") a = [] continue } else if (a.length > 0 && abs(y - a[a.length - 1][1])/delta > 200 ) { if (a.length > 0) dashpath(a, null, null, "5 5") a = [] continue } else a[a.length] = [t, y] } dashpath(a, null, null, "5 5") } else if (s1.substring(0, 1) == "x" && s1.indexOf("=") > 0) { s1 = s1.substring(s1.indexOf("=") + 1) s1 = s1.replace(/y/g, "x") sx = parseEqn(s1) delta = (y2 - y1)/200; var a = [] with (Math) for (var t = y1; less(t, y2+delta); t += delta) { x = eval(sx); if (x == undefined || x == Number.NaN) { if (a.length > 0) dashpath(a, null, null, "5 5") a = [] continue } else if (a.length > 0 && abs(x - a[a.length - 1][1])/delta > 200 ) { if (a.length > 0) dashpath(a, null, null, "5 5") a = [] continue } else a[a.length] = [x, t] } dashpath(a, null, null, "5 5") } } stroke = color var a = [] var sf = fnF.replace(/^\s*/,"") while (sf.indexOf("theta") >= 0) sf = sf.replace(/theta/,"t") var sx = parseEqn("(" + sf + ")cos(t)") var sy = parseEqn("(" + sf + ")sin(t)") delta = (eval(t2) - eval(t1))/200; with (Math) { var t for (t = t1; less(t, t2); t += delta) { x = eval(sx) y = eval(sy) if (y == undefined || y == Number.NaN || x == undefined || x == Number.NaN) { if (a.length > 0) path(a) a = [] continue } else if (a.length > 0 && abs(y - a[a.length - 1][1])/delta > 200 ) { if (a.length > 0) path(a) a = [] continue } else a[a.length] = [x, y] } t = t2 x = eval(sx); y = eval(sy); if (y == undefined || y == Number.NaN || x == undefined || x == Number.NaN) a[a.length] = [x, y] } path(a) } } function drawPolarEqnCurveWithAsymptotics(figName, eqnF, asyms, sx1, sx2, sy1, sy2, dr1, dr2, dt1, dt2, dx1, dx2, dy1, dy2, xstep, ystep, color) { var wx1, wx2, wy1, wy2 var r1, r2, t1, t2, x1, x2, y1, y2 var xs, ys with (Math) { wx1 = eval(parseEqn(sx1)) wx2 = eval(parseEqn(sx2)) wy1 = eval(parseEqn(sy1)) wy2 = eval(parseEqn(sy2)) r1 = eval(parseEqn(dr1)) r2 = eval(parseEqn(dr2)) t1 = eval(parseEqn(dt1)) t2 = eval(parseEqn(dt2)) x1 = eval(parseEqn(dx1)) x2 = eval(parseEqn(dx2)) y1 = eval(parseEqn(dy1)) y2 = eval(parseEqn(dy2)) xs = eval(parseEqn(xstep)) ys = eval(parseEqn(ystep)) } if (wx1 < wx2 && wy1 < wy2) { initPicture(figName, wx1, wx2, wy1, wy2) axes() stroke = "silver" text([wx2 - (wx2 - wx1)/100.0, 0],"x","below","x-axis"); text([0, wy2 - (wy2 - wy1)/100.0],"y","left","y-axis"); text([0, 0],"O","belowleft","origin-mark"); with (Math) { var deltaX = 0.5 var deltaY = 0.5 if (xs > 0) deltaX = xs if (ys > 0) deltaY = ys var bound = sqrt(wx2*wx2 + wy2*wy2) // bound = sqrt(wx1*wx1 + wy1*wy1) > bound ? sqrt(wx1*wx1 + wy1*wy1) : bound // bound = sqrt(wx1*wx1 + wy2*wy2) > bound ? sqrt(wx1*wx1 + wy2*wy2) : bound // bound = sqrt(wx2*wx2 + wy1*wy1) > bound ? sqrt(wx2*wx2 + wy1*wy1) : bound // alert(floor(bound/6)/2) for (var t = deltaX; less(t, bound + deltaX); t += deltaX) { dashcircle([0,0], t, "3 5", ""); text2([t, 0], ""+t, "Arial", "", 12,"below",""); text2([-t, 0], ""+(-t), "Arial", "", 12,"below",""); } for (var t = deltaY; less(t, bound + deltaY); t += deltaY) { text2([0, t], ""+t, "Arial", "", 12,"left",""); text2([0, -t], ""+(-t), "Arial", "", 12,"left",""); } for (var t = pi/12; less(t, pi/4); t += pi/12) { dashline([0,0], [wx2, tan(t)*wx2], "3 5", ""); dashline([0,0], [wx2, -tan(t)*wx2], "3 5", ""); dashline([0,0], [wx1, tan(t)*wx1], "3 5", ""); dashline([0,0], [wx1, -tan(t)*wx1], "3 5", ""); } for (var t = pi/4; less(t, pi/2); t += pi/12) { dashline([0,0], [cot(t)*wx2, wy2], "3 5", ""); dashline([0,0], [cot(t)*wx2, -wy2], "3 5", ""); dashline([0,0], [cot(t)*wx1, wy1], "3 5", ""); dashline([0,0], [cot(t)*wx1, -wy1], "3 5", ""); } } // marker = "blue" var s1 var sy, sx var y, x var delta for (var i = 0; i < asyms.length; i++) { s1 = asyms[i] s1 = s1.replace(/^\s+/,"") stroke = "gray" if (s1.substring(0, 1) == "y" && s1.indexOf("=") > 0) { s1 = s1.substring(s1.indexOf("=") + 1) sy = parseEqn(s1) delta = (x2 - x1)/200; var a = [] with (Math) for (var t = x1; less(t, x2+delta); t += delta) { y = eval(sy); if (y == undefined || y == Number.NaN) { if (a.length > 0) dashpath(a, null, null, "5 5") a = [] continue } else if (a.length > 0 && abs(y - a[a.length - 1][1])/delta > 200 ) { if (a.length > 0) dashpath(a, null, null, "5 5") a = [] continue } else a[a.length] = [t, y] } dashpath(a, null, null, "5 5") } else if (s1.substring(0, 1) == "x" && s1.indexOf("=") > 0) { s1 = s1.substring(s1.indexOf("=") + 1) s1 = s1.replace(/y/g, "x") sx = parseEqn(s1) delta = (y2 - y1)/200; var a = [] with (Math) for (var t = y1; less(t, y2+delta); t += delta) { x = eval(sx); if (x == undefined || x == Number.NaN) { if (a.length > 0) dashpath(a, null, null, "5 5") a = [] continue } else if (a.length > 0 && abs(x - a[a.length - 1][1])/delta > 200 ) { if (a.length > 0) dashpath(a, null, null, "5 5") a = [] continue } else a[a.length] = [x, t] } dashpath(a, null, null, "5 5") } } stroke = color var a = [] var sf = eqnF.replace(/^\s+/,"") if (sf.substring(0, 1) == "r" && sf.indexOf("=") > 0) { sf = sf.substring(sf.indexOf("=") + 1) sy = parseEqn(sf) while (sf.indexOf("theta") >= 0) sf = sf.replace(/theta/,"t") var sx = parseEqn("(" + sf + ")cos(t)") var sy = parseEqn("(" + sf + ")sin(t)") delta = (eval(t2) - eval(t1))/200; with (Math) { var t for (t = t1; less(t, t2); t += delta) { x = eval(sx) y = eval(sy) if (y == undefined || y == Number.NaN || x == undefined || x == Number.NaN) { if (a.length > 0) path(a) a = [] continue } else if (a.length > 0 && abs(y - a[a.length - 1][1])/delta > 200 ) { if (a.length > 0) path(a) a = [] continue } else a[a.length] = [x, y] } t = t2 x = eval(sx); y = eval(sy); if (y == undefined || y == Number.NaN || x == undefined || x == Number.NaN) a[a.length] = [x, y] } path(a) } else if (sf.substring(0, 5) == "theta" && sf.indexOf("=") > 0) { sf = sf.substring(sf.indexOf("=") + 1) sf = parseEqn(sf) while (sf.indexOf("r") >= 0) sf = sf.replace(/r/,"t") var sx = parseEqn("t*cos(" + sf + ")") var sy = parseEqn("t*sin(" + sf + ")") delta = (eval(t2) - eval(t1))/200; with (Math) { var t for (t = r1; less(t, r2); t += delta) { x = eval(sx) y = eval(sy) if (y == undefined || y == Number.NaN || x == undefined || x == Number.NaN) { if (a.length > 0) path(a) a = [] continue } else if (a.length > 0 && abs(y - a[a.length - 1][1])/delta > 200 ) { if (a.length > 0) path(a) a = [] continue } else a[a.length] = [x, y] } t = t2 x = eval(sx); y = eval(sy); if (y == undefined || y == Number.NaN || x == undefined || x == Number.NaN) a[a.length] = [x, y] } path(a) } } }