坐标战舰游戏
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①这个范例演示了一个使用笛卡尔坐标系的经典战舰游戏,玩家需要通过坐标猜测计算机对手的隐藏战舰位置;②涉及的核心数学概念包括坐标系的运用、点的位置判断、集合操作和条件逻辑;③从构造摘要中提炼,范例使用了 Sequence(序列生成)、Intersection(交集计算)、Zip(组合数据)、If(条件判断)、Join(连接字符串)、Shuffle(随机排序)、Polygon(多边形绘制)、PointIn(点在图形内判断)、RandomElement(随机元素选择)、Textfield(文本输入框)、Segment(线段绘制)、TextToUnicode(文本转Unicode)、Defined(定义判断)、Length(长度计算)、Sort(排序)、Corner(角落获取)等 GeoGebra 命令和对象;④适合初中及以上学生,用于练习和巩固笛卡尔坐标系的应用,增强空间想象力和逻辑思维能力。
GeoGebra 命令及参数
Sequence((x(osubhits(1)), n), n, -5, y(osubhits(1)) - 1, 1) → subtargetsd1Sequence((x(osubhits(1)), n), n, y(osubhits(1)) + 1, 5, 1) → subtargetsu1Sequence((n, y(osubhits(1))), n, -5, x(osubhits(1)) - 1, 1) → subtargetsl1Sequence((n, y(osubhits(1))), n, x(osubhits(1)) + 1, 5, 1) → subtargetsr1Intersection(subtargetsd1, alloshots \ osubhits) → subtargetsd2Zip(Segment[osubhits(1), n], n, subtargetsd2) → subtargetlengthsdIf(subtargetlengthdshortest < 2, subtargetlengthdshortest, 2) → subtargetlengthdSequence((x(osubhits(1)), y(osubhits(1)) - n), n, 1, subtargetlengthd, 1) → subtargetsdIntersection(subtargetsu1, alloshots \ osubhits) → subtargetsu2Zip(Segment[osubhits(1), n], n, subtargetsu2) → subtargetlengthsuIf(subtargetlengthushortest < 2, subtargetlengthushortest, 2) → subtargetlengthuSequence((x(osubhits(1)), y(osubhits(1)) + n), n, 1, subtargetlengthu, 1) → subtargetsuIntersection(Join[{subtargetsu, subtargetsd}], AllPoints) → subtargetsv1Intersection(subtargetsl1, alloshots \ osubhits) → subtargetsl2Zip(Segment[osubhits(1), n], n, subtargetsl2) → subtargetlengthslIf(subtargetlengthlshortest < 2, subtargetlengthlshortest, 2) → subtargetlengthlSequence((x(osubhits(1) - n), y(osubhits(1))), n, 1, subtargetlengthl, 1) → subtargetslIntersection(subtargetsr1, alloshots \ osubhits) → subtargetsr2Zip(Segment[osubhits(1), n], n, subtargetsr2) → subtargetlengthsrIf(subtargetlengthrshortest < 2, subtargetlengthrshortest, 2) → subtargetlengthrSequence((x(osubhits(1) + n), y(osubhits(1))), n, 1, subtargetlengthr, 1) → subtargetsrIntersection(Join[{subtargetsr, subtargetsl}], AllPoints) → subtargetsh1If(Length[subtargetsv1] < 2, {}, If[Length[Intersection[subtargetsh1, osubhits]] > 0, {}, subtargetsv1]) → subtargetsv2If(Length[subtargetsh1] < 2, {}, If[Length[Intersection[subtargetsv1, osubhits]] > 0, {}, subtargetsh1]) → subtargetsh2Join({subtargetsh2, subtargetsv2, {(10, 10)}}) → subtargets1Shuffle(subtargets1) → subtargets2, {(10, 10)}Sequence((x(odestroyerhits(1)), n), n, -5, y(odestroyerhits(1)) - 1, 1) → destroyertargetsd1Sequence((x(odestroyerhits(1)), n), n, y(odestroyerhits(1)) + 1, 5, 1) → destroyertargetsu1Sequence((n, y(odestroyerhits(1))), n, -5, x(odestroyerhits(1)) - 1, 1) → destroyertargetsl1Sequence((n, y(odestroyerhits(1))), n, x(odestroyerhits(1)) + 1, 5, 1) → destroyertargetsr1Intersection(destroyertargetsd1, alloshots \ odestroyerhits) → destroyertargetsd2Zip(Segment[odestroyerhits(1), n], n, destroyertargetsd2) → destroyertargetlengthsdIf(destroyertargetlengthdshortest < 1, destroyertargetlengthdshortest, 1) → destroyertargetlengthdSequence((x(odestroyerhits(1)), y(odestroyerhits(1)) - n), n, 1, destroyertargetlengthd, 1) → destroyertargetsdIntersection(destroyertargetsu1, alloshots \ odestroyerhits) → destroyertargetsu2Zip(Segment[odestroyerhits(1), n], n, destroyertargetsu2) → destroyertargetlengthsuIf(destroyertargetlengthushortest < 1, destroyertargetlengthushortest, 1) → destroyertargetlengthuSequence((x(odestroyerhits(1)), y(odestroyerhits(1)) + n), n, 1, destroyertargetlengthu, 1) → destroyertargetsuIntersection(Join[{destroyertargetsu, destroyertargetsd}], AllPoints) → destroyertargetsv1Intersection(destroyertargetsl1, alloshots \ odestroyerhits) → destroyertargetsl2Zip(Segment[odestroyerhits(1), n], n, destroyertargetsl2) → destroyertargetlengthslIf(destroyertargetlengthlshortest < 1, destroyertargetlengthlshortest, 1) → destroyertargetlengthlSequence((x(odestroyerhits(1) - n), y(odestroyerhits(1))), n, 1, destroyertargetlengthl, 1) → destroyertargetslIntersection(destroyertargetsr1, alloshots \ odestroyerhits) → destroyertargetsr2Zip(Segment[odestroyerhits(1), n], n, destroyertargetsr2) → destroyertargetlengthsrIf(destroyertargetlengthrshortest < 1, destroyertargetlengthrshortest, 1) → destroyertargetlengthrSequence((x(odestroyerhits(1) + n), y(odestroyerhits(1))), n, 1, destroyertargetlengthr, 1) → destroyertargetsrIntersection(Join[{destroyertargetsr, destroyertargetsl}], AllPoints) → destroyertargetsh1If(Length[destroyertargetsv1] < 1, {}, If[Length[Intersection[destroyertargetsh1, odestroyerhits]] > 0, {}, destroyertargetsv1]) → destroyertargetsv2If(Length[destroyertargetsh1] < 1, {}, If[Length[Intersection[destroyertargetsv1, odestroyerhits]] > 0, {}, destroyertargetsh1]) → destroyertargetsh2Join({destroyertargetsh2, destroyertargetsv2, {(10, 10)}}) → destroyertargets1Shuffle(destroyertargets1) → destroyertargets2, {(10, 10)}Sequence((x(ocruiserhits(1)), n), n, -5, y(ocruiserhits(1)) - 1, 1) → cruisertargetsd1Sequence((x(ocruiserhits(1)), n), n, y(ocruiserhits(1)) + 1, 5, 1) → cruisertargetsu1Sequence((n, y(ocruiserhits(1))), n, -5, x(ocruiserhits(1)) - 1, 1) → cruisertargetsl1Sequence((n, y(ocruiserhits(1))), n, x(ocruiserhits(1)) + 1, 5, 1) → cruisertargetsr1Intersection(cruisertargetsd1, alloshots \ ocruiserhits) → cruisertargetsd2Zip(Segment[ocruiserhits(1), n], n, cruisertargetsd2) → cruisertargetlengthsdIf(cruisertargetlengthdshortest < 2, cruisertargetlengthdshortest, 2) → cruisertargetlengthdSequence((x(ocruiserhits(1)), y(ocruiserhits(1)) - n), n, 1, cruisertargetlengthd, 1) → cruisertargetsdIntersection(cruisertargetsu1, alloshots \ ocruiserhits) → cruisertargetsu2Zip(Segment[ocruiserhits(1), n], n, cruisertargetsu2) → cruisertargetlengthsuIf(cruisertargetlengthushortest < 2, cruisertargetlengthushortest, 2) → cruisertargetlengthuSequence((x(ocruiserhits(1)), y(ocruiserhits(1)) + n), n, 1, cruisertargetlengthu, 1) → cruisertargetsuIntersection(Join[{cruisertargetsu, cruisertargetsd}], AllPoints) → cruisertargetsv1Intersection(cruisertargetsl1, alloshots \ ocruiserhits) → cruisertargetsl2Zip(Segment[ocruiserhits(1), n], n, cruisertargetsl2) → cruisertargetlengthslIf(cruisertargetlengthlshortest < 2, cruisertargetlengthlshortest, 2) → cruisertargetlengthlSequence((x(ocruiserhits(1) - n), y(ocruiserhits(1))), n, 1, cruisertargetlengthl, 1) → cruisertargetslIntersection(cruisertargetsr1, alloshots \ ocruiserhits) → cruisertargetsr2Zip(Segment[ocruiserhits(1), n], n, cruisertargetsr2) → cruisertargetlengthsrIf(cruisertargetlengthrshortest < 2, cruisertargetlengthrshortest, 2) → cruisertargetlengthrSequence((x(ocruiserhits(1) + n), y(ocruiserhits(1))), n, 1, cruisertargetlengthr, 1) → cruisertargetsrIntersection(Join[{cruisertargetsr, cruisertargetsl}], AllPoints) → cruisertargetsh1If(Length[cruisertargetsv1] < 2, {}, If[Length[Intersection[cruisertargetsh1, ocruiserhits]] > 0, {}, cruisertargetsv1]) → cruisertargetsv2If(Length[cruisertargetsh1] < 2, {}, If[Length[Intersection[cruisertargetsv1, ocruiserhits]] > 0, {}, cruisertargetsh1]) → cruisertargetsh2Join({cruisertargetsh2, cruisertargetsv2, {(10, 10)}}) → cruisertargets1Shuffle(cruisertargets1) → cruisertargets2, {(10, 10)}Sequence((x(ocarrierhits(1)), n), n, -5, y(ocarrierhits(1)) - 1, 1) → carriertargetsd1Sequence((x(ocarrierhits(1)), n), n, y(ocarrierhits(1)) + 1, 5, 1) → carriertargetsu1Sequence((n, y(ocarrierhits(1))), n, -5, x(ocarrierhits(1)) - 1, 1) → carriertargetsl1Sequence((n, y(ocarrierhits(1))), n, x(ocarrierhits(1)) + 1, 5, 1) → carriertargetsr1Intersection(carriertargetsd1, alloshots \ ocarrierhits) → carriertargetsd2Zip(Segment[ocarrierhits(1), n], n, carriertargetsd2) → carriertargetlengthsdIf(carriertargetlengthdshortest < 4, carriertargetlengthdshortest, 4) → carriertargetlengthdSequence((x(ocarrierhits(1)), y(ocarrierhits(1)) - n), n, 1, carriertargetlengthd, 1) → carriertargetsdIntersection(carriertargetsu1, alloshots \ ocarrierhits) → carriertargetsu2Zip(Segment[ocarrierhits(1), n], n, carriertargetsu2) → carriertargetlengthsuIf(carriertargetlengthushortest < 4, carriertargetlengthushortest, 4) → carriertargetlengthuSequence((x(ocarrierhits(1)), y(ocarrierhits(1)) + n), n, 1, carriertargetlengthu, 1) → carriertargetsuIntersection(Join[{carriertargetsu, carriertargetsd}], AllPoints) → carriertargetsv1Intersection(carriertargetsl1, alloshots \ ocarrierhits) → carriertargetsl2Zip(Segment[ocarrierhits(1), n], n, carriertargetsl2) → carriertargetlengthslIf(carriertargetlengthlshortest < 4, carriertargetlengthlshortest, 4) → carriertargetlengthlSequence((x(ocarrierhits(1) - n), y(ocarrierhits(1))), n, 1, carriertargetlengthl, 1) → carriertargetslIntersection(carriertargetsr1, alloshots \ ocarrierhits) → carriertargetsr2Zip(Segment[ocarrierhits(1), n], n, carriertargetsr2) → carriertargetlengthsrIf(carriertargetlengthrshortest < 4, carriertargetlengthrshortest, 4) → carriertargetlengthrSequence((x(ocarrierhits(1) + n), y(ocarrierhits(1))), n, 1, carriertargetlengthr, 1) → carriertargetsrIntersection(Join[{carriertargetsr, carriertargetsl}], AllPoints) → carriertargetsh1If(Length[carriertargetsv1] < 4, {}, If[Length[Intersection[carriertargetsh1, ocarrierhits]] > 0, {}, carriertargetsv1]) → carriertargetsv2If(Length[carriertargetsh1] < 4, {}, If[Length[Intersection[carriertargetsv1, ocarrierhits]] > 0, {}, carriertargetsh1]) → carriertargetsh2Join({carriertargetsh2, carriertargetsv2, {(10, 10)}}) → carriertargets1Shuffle(carriertargets1) → carriertargets2, {(10, 10)}Sequence((x(obattlehits(1)), n), n, -5, y(obattlehits(1)) - 1, 1) → battletargetsd1Sequence((x(obattlehits(1)), n), n, y(obattlehits(1)) + 1, 5, 1) → battletargetsu1Sequence((n, y(obattlehits(1))), n, -5, x(obattlehits(1)) - 1, 1) → battletargetsl1Sequence((n, y(obattlehits(1))), n, x(obattlehits(1)) + 1, 5, 1) → battletargetsr1Intersection(battletargetsd1, alloshots \ obattlehits) → battletargetsd2Zip(Segment[obattlehits(1), n], n, battletargetsd2) → battletargetlengthsdIf(battletargetlengthdshortest < 3, battletargetlengthdshortest, 3) → battletargetlengthdSequence((x(obattlehits(1)), y(obattlehits(1)) - n), n, 1, battletargetlengthd, 1) → battletargetsdIntersection(battletargetsu1, alloshots \ obattlehits) → battletargetsu2Zip(Segment[obattlehits(1), n], n, battletargetsu2) → battletargetlengthsuIf(battletargetlengthushortest < 3, battletargetlengthushortest, 3) → battletargetlengthuSequence((x(obattlehits(1)), y(obattlehits(1)) + n), n, 1, battletargetlengthu, 1) → battletargetsuIntersection(Join[{battletargetsu, battletargetsd}], AllPoints) → battletargetsv1Intersection(battletargetsl1, alloshots \ obattlehits) → battletargetsl2Zip(Segment[obattlehits(1), n], n, battletargetsl2) → battletargetlengthslIf(battletargetlengthlshortest < 3, battletargetlengthlshortest, 3) → battletargetlengthlSequence((x(obattlehits(1) - n), y(obattlehits(1))), n, 1, battletargetlengthl, 1) → battletargetslIntersection(battletargetsr1, alloshots \ obattlehits) → battletargetsr2Zip(Segment[obattlehits(1), n], n, battletargetsr2) → battletargetlengthsrIf(battletargetlengthrshortest < 3, battletargetlengthrshortest, 3) → battletargetlengthrSequence((x(obattlehits(1) + n), y(obattlehits(1))), n, 1, battletargetlengthr, 1) → battletargetsrIntersection(Join[{battletargetsr, battletargetsl}], AllPoints) → battletargetsh1If(Length[battletargetsv1] < 3, {}, If[Length[Intersection[battletargetsh1, obattlehits]] > 0, {}, battletargetsv1]) → battletargetsv2If(Length[battletargetsh1] < 3, {}, If[Length[Intersection[battletargetsv1, obattlehits]] > 0, {}, battletargetsh1]) → battletargetsh2Join({battletargetsh2, battletargetsv2, {(10, 10)}}) → battletargets1Shuffle(battletargets1) → battletargets2, {(10, 10)}Polygon(E, F, G, H) → q2, e, f, g, hPolygon(A, B, C, D) → q1, a, b, c, dPointIn(q2) → subIf(suborient, {sub + (0, 0), sub + (1, 0), sub + (2, 0)}, {sub + (0, 0), sub + (0, 1), sub + (0, 2)}) → subpointsPointIn(q2) → carrierIf(carrierorient, {carrier + (0, 0), carrier + (1, 0), carrier + (2, 0), carrier + (3, 0), carrier + (4, 0)}, {carrier + (0, 0), carrier + (0, 1), carrier + (0, 2), carrier + (0, 3), carrier + (0, 4)}) → carrierpointsPointIn(q2) → battleIf(battleorient, {battle + (0, 0), battle + (1, 0), battle + (2, 0), battle + (3, 0)}, {battle + (0, 0), battle + (0, 1), battle + (0, 2), battle + (0, 3)}) → battlepointsPointIn(q2) → cruiserIf(cruiserorient, {cruiser + (0, 0), cruiser + (1, 0), cruiser + (2, 0)}, {cruiser + (0, 0), cruiser + (0, 1), cruiser + (0, 2)}) → cruiserpointsPointIn(q2) → destroyerIf(destroyerorient, {destroyer + (0, 0), destroyer + (1, 0)}, {destroyer + (0, 0), destroyer + (0, 1)}) → destroyerpointsJoin({subpoints, cruiserpoints, destroyerpoints, carrierpoints, battlepoints}) → AllShipPointsRandomElement(AllPoints) → battleoRandomElement(AllPoints) → carrieroRandomElement(AllPoints) → cruiseroRandomElement(AllPoints) → destroyeroRandomElement(AllPoints) → suboIf(battleoorient, {battleo + (0, 0), battleo + (1, 0), battleo + (2, 0), battleo + (3, 0)}, {battleo + (0, 0), battleo + (0, 1), battleo + (0, 2), battleo + (0, 3)}) → battleopointsIf(carrieroorient, {carriero + (0, 0), carriero + (1, 0), carriero + (2, 0), carriero + (3, 0), carriero + (4, 0)}, {carriero + (0, 0), carriero + (0, 1), carriero + (0, 2), carriero + (0, 3), carriero + (0, 4)}) → carrieropointsIf(cruiseroorient, {cruisero + (0, 0), cruisero + (1, 0), cruisero + (2, 0)}, {cruisero + (0, 0), cruisero + (0, 1), cruisero + (0, 2)}) → cruiseropointsIf(destroyeroorient, {destroyero + (0, 0), destroyero + (1, 0)}, {destroyero + (0, 0), destroyero + (0, 1)}) → destroyeropointsIf(suboorient, {subo + (0, 0), subo + (1, 0), subo + (2, 0)}, {subo + (0, 0), subo + (0, 1), subo + (0, 2)}) → subopointsJoin({battleopoints, carrieropoints, cruiseropoints, destroyeropoints, subopoints}) → AllShipoPointsTextfield(empty) → InputBox1Segment(battleopoints(1), battleopoints(4)) → battleosinkSegment(carrieropoints(1), carrieropoints(5)) → carrierosinkSegment(cruiseropoints(1), cruiseropoints(3)) → cruiserosinkSegment(destroyeropoints(1), destroyeropoints(2)) → destroyerosinkSegment(subopoints(1), subopoints(3)) → subosinkTextToUnicode(empty) → InputUnicodeDefined(IndexOf[44, InputUnicode]) → inputcommaLength(GuessRemain) → iPolygon(I, J, K, L) → q3, i_1, j, k, lSegment(carrierpoints(1), carrierpoints(5)) → carrierlineSegment(battlepoints(1), battlepoints(4)) → battlelineSegment(subpoints(1), subpoints(3)) → sublineSegment(cruiserpoints(1), cruiserpoints(3)) → cruiserlineSegment(destroyerpoints(1), destroyerpoints(2)) → destroyerlineSegment(carrierpoints(1), carrierpoints(5)) → carriersinkSegment(battlepoints(1), battlepoints(4)) → battlesinkSegment(subpoints(1), subpoints(3)) → subsinkSegment(cruiserpoints(1), cruiserpoints(3)) → cruisersinkSegment(destroyerpoints(1), destroyerpoints(2)) → destroyersinkIf(carrierorient, {(-0.5, -0.4), (4.5, -0.5), (-0.5, 0.5)}, {(-0.4, -0.5), (-0.5, 4.5), (0.5, -0.5)}) → carrierpicIf(battleorient, {(-0.5, -0.4), (3.5, -0.4), (-0.5, 0.4)}, {(-0.4, -0.5), (-0.4, 3.5), (0.4, -0.5)}) → battlepicIf(suborient, {(-0.5, -0.3), (2.5, -0.3), (-0.5, 0.3)}, {(-0.3, -0.5), (-0.3, 2.5), (0.3, -0.5)}) → subpicIf(cruiserorient, {(-0.5, -0.3), (2.5, -0.3), (-0.5, 0.3)}, {(-0.3, -0.5), (-0.3, 2.5), (0.3, -0.5)}) → cruiserpicIf(destroyerorient, {(-0.5, -0.3), (1.5, -0.3), (-0.5, 0.3)}, {(-0.3, -0.5), (-0.3, 1.5), (0.3, -0.5)}) → destroyerpicZip(Length[Segment[ocarrierhits(1), n]], n, carriertargets2) → carriertargets3Sort(carriertargets2, carriertargets3) → carriertargets4Zip(Length[Segment[obattlehits(1), n]], n, battletargets2) → battletargets3Sort(battletargets2, battletargets3) → battletargets4Zip(Length[Segment[ocruiserhits(1), n]], n, cruisertargets2) → cruisertargets3Sort(cruisertargets2, cruisertargets3) → cruisertargets4Zip(Length[Segment[osubhits(1), n]], n, subtargets2) → subtargets3Sort(subtargets2, subtargets3) → subtargets4Zip(Length[Segment[odestroyerhits(1), n]], n, destroyertargets2) → destroyertargets3Sort(destroyertargets2, destroyertargets3) → destroyertargets4Zip(Text[explosion, p - (0.6, 0.3)], p, obattlehits) → battleexplosionZip(Text[explosion, p - (0.6, 0.3)], p, ocarrierhits) → carrierexplosionZip(Text[explosion, p - (0.6, 0.3)], p, ocruiserhits) → cruiserexplosionZip(Text[explosion, p - (0.6, 0.3)], p, odestroyerhits) → destroyerexplosionZip(Text[explosion, p - (0.6, 0.3)], p, osubhits) → subexplosionIf(battleoorient, {(-0.5, -0.4), (3.5, -0.4), (-0.5, 0.4)}, {(-0.4, -0.5), (-0.4, 3.5), (0.4, -0.5)}) → battleopicIf(carrieroorient, {(-0.5, -0.4), (4.5, -0.5), (-0.5, 0.5)}, {(-0.4, -0.5), (-0.5, 4.5), (0.5, -0.5)}) → carrieropicIf(cruiseroorient, {(-0.5, -0.3), (2.5, -0.3), (-0.5, 0.3)}, {(-0.3, -0.5), (-0.3, 2.5), (0.3, -0.5)}) → cruiseropicIf(destroyeroorient, {(-0.5, -0.3), (1.5, -0.3), (-0.5, 0.3)}, {(-0.3, -0.5), (-0.3, 1.5), (0.3, -0.5)}) → destroyeropicIf(suboorient, {(-0.5, -0.3), (2.5, -0.3), (-0.5, 0.3)}, {(-0.3, -0.5), (-0.3, 2.5), (0.3, -0.5)}) → subopicCorner(5) → dims
AI 绘图提示语参考
在一个笛卡尔坐标系中,绘制一个模拟战舰游戏的场景。玩家通过坐标猜测隐藏的战舰位置。首先绘制多个坐标点作为可能的射击目标,然后根据玩家的射击结果,在对应坐标点周围绘制长短不一的线段表示命中或未命中,最后将所有命中点连接成一个封闭区域,并在中心放置一个标记点,展示战舰的位置。
以上提示语为根据原始绘图命令整理而来,仅供参考。