{
"cells": [
{
"cell_type": "markdown",
"id": "f74debd5",
"metadata": {},
"source": [
"# gr201_waves\n",
"here to draw triangles on top of a 2D function in order to hide parts of it.\n",
"\n",
"\n",
"\n",
"**Author:** Otto Schaile \n",
"This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Tuesday, May 19, 2026 at 08:38 PM."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "b0b10f94",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:38:29.565589Z"
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"outputs": [],
"source": [
"%%cpp -d\n",
"#include \"TROOT.h\"\n",
"#include \"TCanvas.h\"\n",
"#include \"TColor.h\"\n",
"#include \"TArc.h\"\n",
"#include \"TGraph.h\"\n",
"#include \"TF2.h\"\n",
"#include \"TLine.h\"\n",
"#include \"TLatex.h\"\n",
"#include \"TMath.h\"\n",
"#include \"TStyle.h\""
]
},
{
"cell_type": "markdown",
"id": "0ff3e085",
"metadata": {},
"source": [
" ______________________________________________________________\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "17b02e01",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:38:29.567947Z",
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"shell.execute_reply": "2026-05-19T20:38:29.571105Z"
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"outputs": [],
"source": [
"%%cpp -d\n",
"Double_t interference( Double_t *x, Double_t *par)\n",
"{\n",
" Double_t x_p2 = x[0] * x[0];\n",
" Double_t d_2 = 0.5 * par[2];\n",
" Double_t ym_p2 = (x[1] - d_2) * (x[1] - d_2);\n",
" Double_t yp_p2 = (x[1] + d_2) * (x[1] + d_2);\n",
" Double_t tpi_l = TMath::Pi() / par[1];\n",
" Double_t amplitude = par[0] * (cos(tpi_l * sqrt(x_p2 + ym_p2))\n",
" + par[3] * cos(tpi_l * sqrt(x_p2 + yp_p2)));\n",
" return amplitude * amplitude;\n",
"}"
]
},
{
"cell_type": "markdown",
"id": "117697af",
"metadata": {},
"source": [
" _____________________________________________________________\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "2a6d5fa8",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:38:29.573462Z",
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"shell.execute_reply": "2026-05-19T20:38:29.576071Z"
}
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"outputs": [],
"source": [
"%%cpp -d\n",
"Double_t result( Double_t *x, Double_t *par)\n",
"{\n",
" Double_t xint[2];\n",
" Double_t maxintens = 0, xcur = 14;\n",
" Double_t dlambda = 0.1 * par[1];\n",
" for(Int_t i=0; i<10; i++){\n",
" xint[0] = xcur;\n",
" xint[1] = x[1];\n",
" Double_t intens = interference(xint, par);\n",
" if(intens > maxintens) maxintens = intens;\n",
" xcur -= dlambda;\n",
" }\n",
" return maxintens;\n",
"}"
]
},
{
"cell_type": "markdown",
"id": "1a4b3a59",
"metadata": {},
"source": [
" Arguments are defined. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "0cb81d6d",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:38:29.578311Z",
"iopub.status.busy": "2026-05-19T20:38:29.578124Z",
"iopub.status.idle": "2026-05-19T20:38:29.921532Z",
"shell.execute_reply": "2026-05-19T20:38:29.921108Z"
}
},
"outputs": [],
"source": [
"Double_t d = 3;\n",
"Double_t lambda = 1;\n",
"Double_t amp = 10;"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "946d8c6b",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:38:29.944482Z",
"iopub.status.busy": "2026-05-19T20:38:29.944304Z",
"iopub.status.idle": "2026-05-19T20:38:30.162912Z",
"shell.execute_reply": "2026-05-19T20:38:30.162379Z"
}
},
"outputs": [],
"source": [
"TCanvas *c1 = new TCanvas(\"gr201_waves\", \"A double slit experiment\", 300, 40, 1004, 759);\n",
"c1->Range(0, -10, 30, 10);\n",
"c1->SetFillColor(0);\n",
"TPad *pad = new TPad(\"pr\", \"pr\", 0.5, 0, 1., 1);\n",
"pad->Range(0, -10, 15, 10);\n",
"pad->Draw();\n",
"\n",
"const Int_t colNum = 30;\n",
"Int_t palette[colNum];\n",
"for (Int_t i = 0; i < colNum; i++) {\n",
" Float_t level = 1.*i/colNum;\n",
" palette[i] = TColor::GetColor((Float_t) TMath::Power(level,0.3), (Float_t) TMath::Power(level,0.3), (Float_t) 0.5*level);\n",
" // palette[i] = 1001+i;\n",
"}\n",
"gStyle->SetPalette(colNum, palette);\n",
"\n",
"c1->cd();"
]
},
{
"cell_type": "markdown",
"id": "33ed044a",
"metadata": {},
"source": [
"For the incoming waves, on the left side, we use a TF2 and increase the number\n",
"of points used for drawing to 200 (default is 100) for better resolution"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "a3a4b408",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:38:30.165086Z",
"iopub.status.busy": "2026-05-19T20:38:30.164944Z",
"iopub.status.idle": "2026-05-19T20:38:30.372740Z",
"shell.execute_reply": "2026-05-19T20:38:30.372110Z"
}
},
"outputs": [],
"source": [
"TF2 *f0 = new TF2(\"ray_source\", interference, 0.02, 15, -8, 8, 4);\n",
"f0->SetParameters(amp, lambda, 0, 0);\n",
"f0->SetNpx(200);\n",
"f0->SetNpy(200);\n",
"f0->SetContour(colNum-2);\n",
"f0->Draw(\"samecol\");\n",
"\n",
"TLatex title;\n",
"title.DrawLatex(1.6, 8.5, \"A double slit experiment\");"
]
},
{
"cell_type": "markdown",
"id": "6c839d2f",
"metadata": {},
"source": [
"Draw 2 white triangles to cover parts of f0, simulating a cone\n",
"(change the fill color to see these)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "cf3c3682",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:38:30.375113Z",
"iopub.status.busy": "2026-05-19T20:38:30.374987Z",
"iopub.status.idle": "2026-05-19T20:38:30.582278Z",
"shell.execute_reply": "2026-05-19T20:38:30.581733Z"
}
},
"outputs": [],
"source": [
"TGraph *graph = new TGraph(4);\n",
"graph->SetFillColor(1);\n",
"graph->SetFillStyle(1001);\n",
"graph->SetLineWidth(0);\n",
"graph->SetPoint(0, 0., 0.1);\n",
"graph->SetPoint(1, 14.8, 8);\n",
"graph->SetPoint(2, 0, 8);\n",
"graph->SetPoint(3, 0, 0.1);\n",
"graph->Draw(\"F\");\n",
"\n",
"graph = new TGraph(4);\n",
"graph->SetFillColor(1);\n",
"graph->SetFillStyle(1001);\n",
"graph->SetLineWidth(0);\n",
"graph->SetPoint(0, 0, -0.1);\n",
"graph->SetPoint(1, 14.8, -8);\n",
"graph->SetPoint(2, 0, -8);\n",
"graph->SetPoint(3, 0, -0.1);\n",
"graph->Draw(\"F\");"
]
},
{
"cell_type": "markdown",
"id": "56c99e59",
"metadata": {},
"source": [
"To represent the wall with 2 openings, we draw 3 black vertical lines"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "25f1db62",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:38:30.584790Z",
"iopub.status.busy": "2026-05-19T20:38:30.584661Z",
"iopub.status.idle": "2026-05-19T20:38:30.796469Z",
"shell.execute_reply": "2026-05-19T20:38:30.795928Z"
}
},
"outputs": [],
"source": [
"TLine * line = new TLine(15,-10, 15, 0 - 0.5*d - 0.2);\n",
"line->SetLineWidth(10);\n",
"line->Draw();\n",
"\n",
"line = new TLine(15, 0 - 0.5*d + 0.2, 15, 0 + 0.5*d - 0.2);\n",
"line->SetLineWidth(10);\n",
"line->Draw();\n",
"\n",
"line = new TLine(15, 0 + 0.5*d + 0.2, 15, 10);\n",
"line->SetLineWidth(10);\n",
"line->Draw();\n",
"\n",
"pad->cd();"
]
},
{
"cell_type": "markdown",
"id": "35a25cf7",
"metadata": {},
"source": [
"Interference plot, on the centre-right side"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "086afeb2",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:38:30.798668Z",
"iopub.status.busy": "2026-05-19T20:38:30.798531Z",
"iopub.status.idle": "2026-05-19T20:38:31.005817Z",
"shell.execute_reply": "2026-05-19T20:38:31.005367Z"
}
},
"outputs": [],
"source": [
"TF2 *finter = new TF2(\"interference\",interference, 0.01, 14, -10, 10, 4);\n",
"finter->SetParameters(amp, lambda, d, 1);\n",
"finter->SetNpx(200);\n",
"finter->SetNpy(200);\n",
"finter->SetContour(colNum-2);\n",
"finter->Draw(\"samecol\");"
]
},
{
"cell_type": "markdown",
"id": "3ae087ee",
"metadata": {},
"source": [
"Some lines"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "a702a738",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:38:31.019452Z",
"iopub.status.busy": "2026-05-19T20:38:31.019291Z",
"iopub.status.idle": "2026-05-19T20:38:31.231266Z",
"shell.execute_reply": "2026-05-19T20:38:31.230634Z"
}
},
"outputs": [],
"source": [
"TArc arc;\n",
"arc.SetFillStyle(0);\n",
"arc.SetLineWidth(2);\n",
"arc.SetLineColor(5);\n",
"Float_t r = 0.5 * lambda, dr = lambda;\n",
"for (Int_t i = 0; i < 16; i++) {\n",
" arc.DrawArc(0, 0.5*d, r, 0., 360., \"only\");\n",
" arc.DrawArc(0, -0.5*d, r, 0., 360., \"only\");\n",
" r += dr;\n",
"}\n",
"\n",
"pad->cd();"
]
},
{
"cell_type": "markdown",
"id": "f934f894",
"metadata": {},
"source": [
"Result, on the right edge"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "1cbb5ac7",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:38:31.233184Z",
"iopub.status.busy": "2026-05-19T20:38:31.233064Z",
"iopub.status.idle": "2026-05-19T20:38:31.440558Z",
"shell.execute_reply": "2026-05-19T20:38:31.439956Z"
}
},
"outputs": [],
"source": [
"TF2 *fresult = new TF2(\"result\",result, 14, 15, -10, 10, 4);\n",
"fresult->SetParameters(amp, lambda, d, 1);\n",
"fresult->SetNpx(300);\n",
"fresult->SetNpy(300);\n",
"fresult->SetContour(colNum-2);\n",
"fresult->Draw(\"samecol\");"
]
},
{
"cell_type": "markdown",
"id": "71535bfe",
"metadata": {},
"source": [
"Vertical white line on the right side"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "1b4478f0",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:38:31.442446Z",
"iopub.status.busy": "2026-05-19T20:38:31.442321Z",
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"shell.execute_reply": "2026-05-19T20:38:32.703113Z"
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"source": [
"line = new TLine(14,-10, 14, 10);\n",
"line->SetLineWidth(10); line->SetLineColor(0); line->Draw();\n",
"c1->Modified(kTRUE);\n",
"c1->Update();\n",
"c1->SetEditable(kTRUE);"
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},
{
"cell_type": "markdown",
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"source": [
"Draw all canvases "
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"source": [
"gROOT->GetListOfCanvases()->Draw()"
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