3D Implicit Function Plotter
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This example demonstrates 3D graphs of polynomial implicit functions. Key mathematical concepts include implicit functions, polynomial functions, and coordinate geometry. Using GeoGebra commands such as ImplicitCurve, Vector, and Polygon, complex 3D graphs can be constructed. Suitable for high school and above students or teachers.
GeoGebra Commands & Parameters
Corner(1) → Eckpunkt1Corner(2) → Eckpunkt2If(c, α, (x(C - Eckpunkt1) / dEx * c_{Move})) → α1Mod(α1, 6.283) → α2Corner(3) → Eckpunkt3If(c, β, (y(C - Eckpunkt2) / dEy * c_{Move})) → β1Mod(β1, 6.283) → β2Element(lF, Funktion) → g0Sequence((a11' * Element[zWX1, i]) + (a12 * Element[zWY1, i]) + (a13 * Element[zWZ1, i]), i, 1, 4) → zWX1'Element(zWW_0, 3) → zW_2Element(zWW_0, 4) → zW_1Element(zWW_0, 2) → zW_3Polygon(Eckpunkt1, Eck11, Eck12, (x(Eckpunkt1), y(Eck12))) → Vieleck2, eckpunkt1, eck11, eck12, a_1Sequence(Segment[Element[zl10, i], Element[zl10, i + 1]], i, 1, 7) → BoxStrVector(Element[zl10, 4], Element[zl10, 1]) → zVectxVector(Element[zl10, 4], Element[zl10, 3]) → zVectzyVector(Element[zl10, 4], Element[zl10, 5]) → zVectzPolygon(Eck11, Eckpunkt2, Eckpunkt3, Eck12) → Vieleck1, eck11_1, eckpunkt2, eckpunkt3, eck12_1Element(zTT, zW_1) → zY1Element(zTT, zW_2) → zY2Element(zTT, zW_3) → zY3Polygon(zTT) → zTTPolyElement(zl10, zW_1) → zlN11Element(zl10, 9 - zW_1) → zlN111Element(zl10, zW_2) → zlN22Element(zl10, 9 - zW_2) → zlN222Element(zl10, zW_3) → zlN33Element(zWW_0, 1) → zW_4Element(zl10, zW_4) → zlN44Polygon({zlN11, zlN22, zlN222, zlN111}) → Vgrund01Polygon(Sequence[Element[zl10, i], i, 1, 4]) → Vgrund000Element(zl10, 7) → P_RElement(zl10, 8) → P_LPolygon({Element[zl10, 1], Element[zl10, 2], Element[zl10, 7], Element[zl10, 8]}) → Vvrd0Segment(P_R, P_L) → StrRLPolygon(Sequence[Element[zl10, i], i, 9, 12]) → zlPolyRay(B, Element[zl10, 13]) → StryRay(B, Element[zl10, 14]) → StrzyRay(B, Element[zl10, 15]) → StrxTextfield(x_{min}) → inputBox1Textfield(x_{max}) → inputBox4Textfield(v_{Animation}) → inputBox8Textfield(Step) → inputBox7Textfield(N) → inputBox9If(b_2, t, cos(((2 * π) * t0))) → RotIf(b_2, ℯ^(t), sin(((8 * π) * t0))) → GrünIf(b_2, ℯ^((-t)), 1 - t0^(2)) → BlauTextfield(t) → inputBox10Textfield(g00) → textfield1Textfield(Funktion) → Textfeld1ImplicitCurve(wx3(x - x(B), y - y(B), t)) → ex1Vector(B, B2) → uSegment(B1, B) → e_2Polygon(Q1, Q3, Q4, Q2) → poly1, q1, q3, q4, q2Textfield(f) → inputBox2Textfield(Th) → inputBox3Textfield(g) → inputBox5Textfield(Stepg) → inputBox6Sequence(If[i > g, ¬j, j], i, 1, N + 1) → ltrueIf(j, N + 1, 0) → truebImplicitCurve(wx3(x - x(B), y - y(B), (-4))) → M2_{1}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.96))) → M2_{2}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.92))) → M2_{3}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.88))) → M2_{4}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.84))) → M2_{5}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.8))) → M2_{6}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.76))) → M2_{7}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.7199999999999998))) → M2_{8}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.68))) → M2_{9}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.64))) → M2_{10}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.6))) → M2_{11}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.56))) → M2_{12}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.52))) → M2_{13}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.48))) → M2_{14}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.44))) → M2_{15}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.4))) → M2_{16}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.36))) → M2_{17}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.32))) → M2_{18}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.2800000000000002))) → M2_{19}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.24))) → M2_{20}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.2))) → M2_{21}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.16))) → M2_{22}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.12))) → M2_{23}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.08))) → M2_{24}ImplicitCurve(wx3(x - x(B), y - y(B), (-3.04))) → M2_{25}ImplicitCurve(wx3(x - x(B), y - y(B), (-3))) → M2_{26}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.96))) → M2_{27}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.92))) → M2_{28}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.88))) → M2_{29}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.84))) → M2_{30}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.8))) → M2_{31}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.76))) → M2_{32}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.7199999999999998))) → M2_{33}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.6799999999999997))) → M2_{34}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.6399999999999997))) → M2_{35}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.5999999999999996))) → M2_{36}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.56))) → M2_{37}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.52))) → M2_{38}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.48))) → M2_{39}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.44))) → M2_{40}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.4))) → M2_{41}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.36))) → M2_{42}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.3200000000000003))) → M2_{43}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.2800000000000002))) → M2_{44}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.24))) → M2_{45}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.2))) → M2_{46}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.16))) → M2_{47}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.12))) → M2_{48}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.08))) → M2_{49}ImplicitCurve(wx3(x - x(B), y - y(B), (-2.04))) → M2_{50}ImplicitCurve(wx3(x - x(B), y - y(B), (-2))) → M2_{51}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.96))) → M2_{52}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.92))) → M2_{53}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.88))) → M2_{54}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.8399999999999999))) → M2_{55}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.7999999999999998))) → M2_{56}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.7599999999999998))) → M2_{57}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.7199999999999998))) → M2_{58}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.6800000000000002))) → M2_{59}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.6400000000000001))) → M2_{60}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.6))) → M2_{61}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.56))) → M2_{62}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.52))) → M2_{63}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.48))) → M2_{64}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.44))) → M2_{65}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.4))) → M2_{66}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.3599999999999999))) → M2_{67}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.3199999999999998))) → M2_{68}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.2799999999999998))) → M2_{69}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.2399999999999998))) → M2_{70}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.1999999999999997))) → M2_{71}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.1600000000000001))) → M2_{72}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.12))) → M2_{73}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.08))) → M2_{74}ImplicitCurve(wx3(x - x(B), y - y(B), (-1.04))) → M2_{75}ImplicitCurve(wx3(x - x(B), y - y(B), -1)) → M2_{76}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.96))) → M2_{77}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.9199999999999999))) → M2_{78}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.8799999999999999))) → M2_{79}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.8399999999999999))) → M2_{80}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.7999999999999998))) → M2_{81}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.7599999999999998))) → M2_{82}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.7199999999999998))) → M2_{83}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.6799999999999997))) → M2_{84}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.6400000000000001))) → M2_{85}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.6000000000000001))) → M2_{86}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.56))) → M2_{87}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.52))) → M2_{88}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.48))) → M2_{89}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.43999999999999995))) → M2_{90}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.3999999999999999))) → M2_{91}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.3599999999999999))) → M2_{92}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.31999999999999984))) → M2_{93}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.2799999999999998))) → M2_{94}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.23999999999999977))) → M2_{95}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.19999999999999973))) → M2_{96}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.16000000000000014))) → M2_{97}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.1200000000000001))) → M2_{98}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.08000000000000007))) → M2_{99}ImplicitCurve(wx3(x - x(B), y - y(B), (-0.040000000000000036))) → M2_{100}ImplicitCurve(wx3(x - x(B), y - y(B), 0)) → M2_{101}ImplicitCurve(wx3(x - x(B), y - y(B), 0.040000000000000036)) → M2_{102}ImplicitCurve(wx3(x - x(B), y - y(B), 0.08000000000000007)) → M2_{103}ImplicitCurve(wx3(x - x(B), y - y(B), 0.1200000000000001)) → M2_{104}ImplicitCurve(wx3(x - x(B), y - y(B), 0.16000000000000014)) → M2_{105}ImplicitCurve(wx3(x - x(B), y - y(B), 0.20000000000000018)) → M2_{106}ImplicitCurve(wx3(x - x(B), y - y(B), 0.2400000000000002)) → M2_{107}ImplicitCurve(wx3(x - x(B), y - y(B), 0.28000000000000025)) → M2_{108}ImplicitCurve(wx3(x - x(B), y - y(B), 0.3200000000000003)) → M2_{109}ImplicitCurve(wx3(x - x(B), y - y(B), 0.3600000000000003)) → M2_{110}ImplicitCurve(wx3(x - x(B), y - y(B), 0.40000000000000036)) → M2_{111}ImplicitCurve(wx3(x - x(B), y - y(B), 0.4400000000000004)) → M2_{112}ImplicitCurve(wx3(x - x(B), y - y(B), 0.4800000000000004)) → M2_{113}ImplicitCurve(wx3(x - x(B), y - y(B), 0.5200000000000005)) → M2_{114}ImplicitCurve(wx3(x - x(B), y - y(B), 0.5600000000000005)) → M2_{115}ImplicitCurve(wx3(x - x(B), y - y(B), 0.6000000000000005)) → M2_{116}ImplicitCurve(wx3(x - x(B), y - y(B), 0.6399999999999997)) → M2_{117}ImplicitCurve(wx3(x - x(B), y - y(B), 0.6799999999999997)) → M2_{118}ImplicitCurve(wx3(x - x(B), y - y(B), 0.7199999999999998)) → M2_{119}ImplicitCurve(wx3(x - x(B), y - y(B), 0.7599999999999998)) → M2_{120}ImplicitCurve(wx3(x - x(B), y - y(B), 0.7999999999999998)) → M2_{121}ImplicitCurve(wx3(x - x(B), y - y(B), 0.8399999999999999)) → M2_{122}ImplicitCurve(wx3(x - x(B), y - y(B), 0.8799999999999999)) → M2_{123}ImplicitCurve(wx3(x - x(B), y - y(B), 0.9199999999999999)) → M2_{124}ImplicitCurve(wx3(x - x(B), y - y(B), 0.96)) → M2_{125}ImplicitCurve(wx3(x - x(B), y - y(B), 1)) → M2_{126}ImplicitCurve(wx3(x - x(B), y - y(B), 1.04)) → M2_{127}ImplicitCurve(wx3(x - x(B), y - y(B), 1.08)) → M2_{128}ImplicitCurve(wx3(x - x(B), y - y(B), 1.12)) → M2_{129}ImplicitCurve(wx3(x - x(B), y - y(B), 1.1600000000000001)) → M2_{130}ImplicitCurve(wx3(x - x(B), y - y(B), 1.2000000000000002)) → M2_{131}ImplicitCurve(wx3(x - x(B), y - y(B), 1.2400000000000002)) → M2_{132}ImplicitCurve(wx3(x - x(B), y - y(B), 1.2800000000000002)) → M2_{133}ImplicitCurve(wx3(x - x(B), y - y(B), 1.3200000000000003)) → M2_{134}ImplicitCurve(wx3(x - x(B), y - y(B), 1.3600000000000003)) → M2_{135}ImplicitCurve(wx3(x - x(B), y - y(B), 1.4000000000000004)) → M2_{136}ImplicitCurve(wx3(x - x(B), y - y(B), 1.4400000000000004)) → M2_{137}ImplicitCurve(wx3(x - x(B), y - y(B), 1.4800000000000004)) → M2_{138}ImplicitCurve(wx3(x - x(B), y - y(B), 1.5200000000000005)) → M2_{139}ImplicitCurve(wx3(x - x(B), y - y(B), 1.5600000000000005)) → M2_{140}ImplicitCurve(wx3(x - x(B), y - y(B), 1.6000000000000005)) → M2_{141}ImplicitCurve(wx3(x - x(B), y - y(B), 1.6399999999999997)) → M2_{142}ImplicitCurve(wx3(x - x(B), y - y(B), 1.6799999999999997)) → M2_{143}ImplicitCurve(wx3(x - x(B), y - y(B), 1.7199999999999998)) → M2_{144}ImplicitCurve(wx3(x - x(B), y - y(B), 1.7599999999999998)) → M2_{145}ImplicitCurve(wx3(x - x(B), y - y(B), 1.7999999999999998)) → M2_{146}ImplicitCurve(wx3(x - x(B), y - y(B), 1.8399999999999999)) → M2_{147}ImplicitCurve(wx3(x - x(B), y - y(B), 1.88)) → M2_{148}ImplicitCurve(wx3(x - x(B), y - y(B), 1.92)) → M2_{149}ImplicitCurve(wx3(x - x(B), y - y(B), 1.96)) → M2_{150}ImplicitCurve(wx3(x - x(B), y - y(B), 2)) → M2_{151}ImplicitCurve(wx3(x - x(B), y - y(B), 2.04)) → M2_{152}ImplicitCurve(wx3(x - x(B), y - y(B), 2.08)) → M2_{153}ImplicitCurve(wx3(x - x(B), y - y(B), 2.12)) → M2_{154}ImplicitCurve(wx3(x - x(B), y - y(B), 2.16)) → M2_{155}ImplicitCurve(wx3(x - x(B), y - y(B), 2.2)) → M2_{156}ImplicitCurve(wx3(x - x(B), y - y(B), 2.24)) → M2_{157}ImplicitCurve(wx3(x - x(B), y - y(B), 2.2800000000000002)) → M2_{158}ImplicitCurve(wx3(x - x(B), y - y(B), 2.3200000000000003)) → M2_{159}ImplicitCurve(wx3(x - x(B), y - y(B), 2.3600000000000003)) → M2_{160}ImplicitCurve(wx3(x - x(B), y - y(B), 2.4000000000000004)) → M2_{161}ImplicitCurve(wx3(x - x(B), y - y(B), 2.4400000000000004)) → M2_{162}ImplicitCurve(wx3(x - x(B), y - y(B), 2.4800000000000004)) → M2_{163}ImplicitCurve(wx3(x - x(B), y - y(B), 2.5200000000000005)) → M2_{164}ImplicitCurve(wx3(x - x(B), y - y(B), 2.5600000000000005)) → M2_{165}ImplicitCurve(wx3(x - x(B), y - y(B), 2.6000000000000005)) → M2_{166}ImplicitCurve(wx3(x - x(B), y - y(B), 2.6400000000000006)) → M2_{167}ImplicitCurve(wx3(x - x(B), y - y(B), 2.6799999999999997)) → M2_{168}ImplicitCurve(wx3(x - x(B), y - y(B), 2.7199999999999998)) → M2_{169}ImplicitCurve(wx3(x - x(B), y - y(B), 2.76)) → M2_{170}ImplicitCurve(wx3(x - x(B), y - y(B), 2.8)) → M2_{171}ImplicitCurve(wx3(x - x(B), y - y(B), 2.84)) → M2_{172}ImplicitCurve(wx3(x - x(B), y - y(B), 2.88)) → M2_{173}ImplicitCurve(wx3(x - x(B), y - y(B), 2.92)) → M2_{174}ImplicitCurve(wx3(x - x(B), y - y(B), 2.96)) → M2_{175}ImplicitCurve(wx3(x - x(B), y - y(B), 3)) → M2_{176}ImplicitCurve(wx3(x - x(B), y - y(B), 3.04)) → M2_{177}ImplicitCurve(wx3(x - x(B), y - y(B), 3.08)) → M2_{178}ImplicitCurve(wx3(x - x(B), y - y(B), 3.12)) → M2_{179}ImplicitCurve(wx3(x - x(B), y - y(B), 3.16)) → M2_{180}ImplicitCurve(wx3(x - x(B), y - y(B), 3.2)) → M2_{181}ImplicitCurve(wx3(x - x(B), y - y(B), 3.24)) → M2_{182}ImplicitCurve(wx3(x - x(B), y - y(B), 3.2800000000000002)) → M2_{183}ImplicitCurve(wx3(x - x(B), y - y(B), 3.3200000000000003)) → M2_{184}ImplicitCurve(wx3(x - x(B), y - y(B), 3.3600000000000003)) → M2_{185}ImplicitCurve(wx3(x - x(B), y - y(B), 3.4000000000000004)) → M2_{186}ImplicitCurve(wx3(x - x(B), y - y(B), 3.4400000000000004)) → M2_{187}ImplicitCurve(wx3(x - x(B), y - y(B), 3.4800000000000004)) → M2_{188}ImplicitCurve(wx3(x - x(B), y - y(B), 3.5200000000000005)) → M2_{189}ImplicitCurve(wx3(x - x(B), y - y(B), 3.5600000000000005)) → M2_{190}ImplicitCurve(wx3(x - x(B), y - y(B), 3.6000000000000005)) → M2_{191}ImplicitCurve(wx3(x - x(B), y - y(B), 3.6400000000000006)) → M2_{192}ImplicitCurve(wx3(x - x(B), y - y(B), 3.6799999999999997)) → M2_{193}ImplicitCurve(wx3(x - x(B), y - y(B), 3.7199999999999998)) → M2_{194}ImplicitCurve(wx3(x - x(B), y - y(B), 3.76)) → M2_{195}ImplicitCurve(wx3(x - x(B), y - y(B), 3.8)) → M2_{196}ImplicitCurve(wx3(x - x(B), y - y(B), 3.84)) → M2_{197}ImplicitCurve(wx3(x - x(B), y - y(B), 3.88)) → M2_{198}ImplicitCurve(wx3(x - x(B), y - y(B), 3.92)) → M2_{199}ImplicitCurve(wx3(x - x(B), y - y(B), 3.96)) → M2_{200}ImplicitCurve(wx3(x - x(B), y - y(B), 4)) → M2_{201}