{ "app": "MathPad", "version": 3, "nextId": 121, "name": "绘图示例.mpad", "regions": [ { "id": 1, "x": 40, "y": 40, "kind": "text", "latex": "", "text": "绘图示例。所有图点右上角 ⚙（图形选项）都能换图型（折线 / 散点 / 柱状 / 火柴杆 / 面积）、调采样点数、柱宽；鼠标悬停可以读数、拖框放大。多条曲线用分号隔开：plot(f;g, 起, 终)。" }, { "id": 2, "x": 40, "y": 93, "kind": "text", "latex": "", "text": "一、画多条曲线的三种情形" }, { "id": 3, "x": 40, "y": 127, "kind": "text", "latex": "", "text": "① 给定数据集：两组数据共用同一条横轴。先给横轴，再给两组 y，中间用分号隔开,或矩阵形式。" }, { "id": 4, "x": 40, "y": 161, "kind": "math", "latex": "xs:=1,2,3,4,5,6,7,8", "text": "" }, { "id": 5, "x": 40, "y": 211, "kind": "math", "latex": "ya:=3,5,4,7,6,9,8,10", "text": "" }, { "id": 7, "x": 40, "y": 380, "kind": "math", "latex": "plot(ya;yb,xs)", "text": "" }, { "id": 9, "x": 765, "y": 401, "kind": "math", "latex": "plot(4\\sin(x);fd(x),-6,6)", "text": "", "style": { "dash": "solid", "width": 2, "color": "#185FA5", "marker": "none", "msize": 6, "grid": true, "box": true, "title": "", "xlabel": "", "ylabel": "", "titleSize": 14, "xlabelSize": 11, "ylabelSize": 11, "tickSize": 11, "legendPos": "", "legendSize": 11, "xmin": "-5", "xmax": "5", "ymin": "-10", "ymax": "10", "xlog": false, "ylog": false, "axes": true, "xaxisPos": "zero", "yaxisPos": "zero", "colorscale": "", "levels": 10, "labels": true, "barw": 0.6, "chartType": "", "barmode": "group", "bargap": -0.2, "barline": "", "points": "", "bins": "", "w": 560, "h": 300, "page": "", "mrow": 6, "mcol": 6, "exportScale": 2, "channel": "auto", "imgfit": "contain", "interp": "smooth", "azimuth": 1.3, "elevation": 0.6, "fill": false, "fillalpha": "", "series": [] } }, { "id": 11, "x": 60, "y": 1121, "kind": "text", "latex": "", "text": "③ 带未定参数的两条曲线：a、b 从来没定义过，图形框右侧就自动长出两个滑块框（每条曲线一个）。拖一下曲线立刻跟着变，只重算这一个图，不动整篇文档。" }, { "id": 13, "x": 59, "y": 1874, "kind": "text", "latex": "", "text": "参数框里的同名参数默认\"各自独立\"；点参数名前面的链子按钮可以挂到一起，拖一个另一个跟着动。" }, { "id": 14, "x": 40, "y": 1914, "kind": "text", "latex": "", "text": "二、采样点数与数据图" }, { "id": 15, "x": 40, "y": 1947, "kind": "text", "latex": "", "text": "第 4 个参数 = 采样点数：点少是折线粗版，点多才光滑（默认 200）。" }, { "id": 16, "x": 40, "y": 1980, "kind": "math", "latex": "plot(\\sin(x),-6,6,12)", "text": "" }, { "id": 17, "x": 40, "y": 2334, "kind": "text", "latex": "", "text": "只给一组 y 时横轴默认是点序号 0,1,2…；要自己的横轴就把两组数据一起给：plot(xs, ys)。" }, { "id": 18, "x": 40, "y": 2367, "kind": "math", "latex": "v:=\\begin{pmatrix}4\\\\9\\\\2\\\\7\\\\5\\\\8\\end{pmatrix}", "text": "" }, { "id": 19, "x": 40, "y": 2530, "kind": "math", "latex": "plot(v)", "text": "" }, { "id": 20, "x": 40, "y": 2884, "kind": "math", "latex": "xs2:=0, 0.5 .. 2.5", "text": "" }, { "id": 21, "x": 40, "y": 2934, "kind": "math", "latex": "plot(xs2, v)", "text": "" }, { "id": 22, "x": 40, "y": 3288, "kind": "text", "latex": "", "text": "三、柱状图：三组数据并排" }, { "id": 23, "x": 40, "y": 3321, "kind": "text", "latex": "", "text": "分号分数据集 —— 一组一根柱子，同一个位置上的三根并排站。柱宽比例、并排还是堆叠，都在 ⚙ 里调。" }, { "id": 24, "x": 40, "y": 3354, "kind": "math", "latex": "m:=2,4,6,8", "text": "" }, { "id": 25, "x": 40, "y": 3404, "kind": "math", "latex": "q1:=5,7,6,9", "text": "" }, { "id": 26, "x": 40, "y": 3454, "kind": "math", "latex": "q2:=3,4,5,6", "text": "" }, { "id": 27, "x": 40, "y": 3504, "kind": "math", "latex": "q3:=6,5,8,7", "text": "" }, { "id": 28, "x": 40, "y": 3554, "kind": "math", "latex": "bar(q1;q2;q3,m)", "text": "" }, { "id": 29, "x": 40, "y": 3908, "kind": "text", "latex": "", "text": "四、其它统计图型（同一个 ⚙ 里也能互相切换）" }, { "id": 30, "x": 40, "y": 3941, "kind": "math", "latex": "stem(v)", "text": "" }, { "id": 31, "x": 40, "y": 4295, "kind": "math", "latex": "area(v)", "text": "" }, { "id": 32, "x": 40, "y": 4649, "kind": "math", "latex": "pie(3,5,2,6)", "text": "" }, { "id": 33, "x": 40, "y": 5043, "kind": "math", "latex": "scatter(x\\text{\\textasciicircum}^{2},-3,3)", "text": "" }, { "id": 34, "x": 40, "y": 5397, "kind": "text", "latex": "", "text": "五、坐标与极坐标" }, { "id": 35, "x": 40, "y": 5430, "kind": "math", "latex": "loglog(x\\text{\\textasciicircum}^{3},1,10)", "text": "", "style": { "dash": "solid", "width": 2, "color": "#185FA5", "marker": "none", "msize": 6, "grid": true, "box": true, "title": "", "xlabel": "", "ylabel": "", "titleSize": 14, "xlabelSize": 11, "ylabelSize": 11, "tickSize": 11, "legendPos": "", "legendSize": 11, "xmin": "0", "xmax": "1", "ymin": "", "ymax": "", "xlog": false, "ylog": false, "axes": true, "xaxisPos": "edge", "yaxisPos": "edge", "colorscale": "", "levels": 10, "labels": true, "barw": 0.6, "chartType": "", "barmode": "group", "bargap": -0.2, "barline": "", "points": "", "bins": "", "w": 560, "h": 300, "page": "", "mrow": 6, "mcol": 6, "exportScale": 2, "channel": "auto", "imgfit": "contain", "interp": "smooth", "azimuth": 1.3, "elevation": 0.6, "fill": false, "fillalpha": "", "series": [] } }, { "id": 36, "x": 40, "y": 5784, "kind": "math", "latex": "polar(\\sin(3t),0,6.28)", "text": "", "pv": { "g0:omega": -5.85 } }, { "id": 37, "x": 40, "y": 6138, "kind": "text", "latex": "", "text": "六、三维与场" }, { "id": 38, "x": 40, "y": 6171, "kind": "text", "latex": "", "text": "曲面用同心水波更直观：sin(√(x²+y²)) 一眼就是立体的；热力图换成棋盘格 sin(x)·cos(y) —— 亮暗相间一眼看懂。" }, { "id": 39, "x": 40, "y": 6204, "kind": "math", "latex": "surf(\\sin\\left(\\sqrt{x\\text{\\textasciicircum}^{2}+y\\text{\\textasciicircum}^{2}}\\right),-8,8)", "text": "", "style": { "dash": "solid", "width": 2, "color": "#185FA5", "marker": "none", "msize": 6, "grid": true, "box": true, "title": "", "xlabel": "", "ylabel": "", "titleSize": 14, "xlabelSize": 11, "ylabelSize": 11, "tickSize": 11, "legendPos": "", "legendSize": 11, "xmin": "", "xmax": "", "ymin": "", "ymax": "", "xlog": false, "ylog": false, "axes": true, "xaxisPos": "edge", "yaxisPos": "edge", "colorscale": "Jet", "levels": 10, "labels": true, "barw": 0.6, "chartType": "", "barmode": "group", "bargap": -0.2, "barline": "", "points": "", "bins": "", "w": 560, "h": 300, "page": "", "mrow": 6, "mcol": 6, "exportScale": 2, "channel": "auto", "imgfit": "contain", "interp": "smooth", "azimuth": 1.3, "elevation": 0.6, "fill": false, "fillalpha": "", "series": [] } }, { "id": 40, "x": 40, "y": 6679, "kind": "math", "latex": "contour(a\\times x\\text{\\textasciicircum}^2+b\\times y\\text{\\textasciicircum}^2,-2,2)", "text": "", "pv": { "g0:a": -4.12, "g0:b": -7.58 } }, { "id": 41, "x": 40, "y": 7113, "kind": "math", "latex": "heatmap(\\sin(x)\\cdot\\cos(y),-6,6)", "text": "" }, { "id": 42, "x": 40, "y": 7547, "kind": "math", "latex": "quiver(-y,x,-2,2)", "text": "" }, { "id": 43, "x": 40, "y": 7901, "kind": "text", "latex": "", "text": "提示：数据处理的图（直方图 hist、频谱 plot(fft(…))）见 信号变换示例；图像处理相关见 图像处理示例。" }, { "id": 44, "x": 40, "y": 7934, "kind": "text", "latex": "", "text": "七、三维曲面上的参数滑块" }, { "id": 45, "x": 40, "y": 7967, "kind": "text", "latex": "", "text": "3D 曲面、热力图、等值线、饼图、极坐标、散点……所有图型都一样：拖 a、b 看曲面怎么变形（多张曲面之间同名参数同样各自动，也能用链子挂到一起）。" }, { "id": 47, "x": 57, "y": 8560, "kind": "math", "latex": "heatmap(a\\cdot x\\text{\\textasciicircum}^{2}+b\\cdot 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