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// Copyright © 2016 Alan A. A. Donovan & Brian W. Kernighan.
// License: https://creativecommons.org/licenses/by-nc-sa/4.0/

// See page 203.

// The surface program plots the 3-D surface of a user-provided function.
package main

import (
    "fmt"
    "io"
    "log"
    "math"
    "net/http"
)

//!+parseAndCheck
import "gopl.io/ch7/eval"

//!-parseAndCheck

// -- copied from gopl.io/ch3/surface --

const (
    width, height = 600, 320            // canvas size in pixels
    cells         = 100                 // number of grid cells
    xyrange       = 30.0                // x, y axis range (-xyrange..+xyrange)
    xyscale       = width / 2 / xyrange // pixels per x or y unit
    zscale        = height * 0.4        // pixels per z unit
)

var sin30, cos30 = 0.5, math.Sqrt(3.0 / 4.0) // sin(30°), cos(30°)

func corner(f func(x, y float64) float64, i, j int) (float64, float64) {
    // find point (x,y) at corner of cell (i,j)
    x := xyrange * (float64(i)/cells - 0.5)
    y := xyrange * (float64(j)/cells - 0.5)

    z := f(x, y) // compute surface height z

    // project (x,y,z) isometrically onto 2-D SVG canvas (sx,sy)
    sx := width/2 + (x-y)*cos30*xyscale
    sy := height/2 + (x+y)*sin30*xyscale - z*zscale
    return sx, sy
}

func surface(w io.Writer, f func(x, y float64) float64) {
    fmt.Fprintf(w, "<svg xmlns='http://www.w3.org/2000/svg' "+
        "style='stroke: grey; fill: white; stroke-width: 0.7' "+
        "width='%d' height='%d'>", width, height)
    for i := 0; i < cells; i++ {
        for j := 0; j < cells; j++ {
            ax, ay := corner(f, i+1, j)
            bx, by := corner(f, i, j)
            cx, cy := corner(f, i, j+1)
            dx, dy := corner(f, i+1, j+1)
            fmt.Fprintf(w, "<polygon points='%g,%g %g,%g %g,%g %g,%g'/>\n",
                ax, ay, bx, by, cx, cy, dx, dy)
        }
    }
    fmt.Fprintln(w, "</svg>")
}

// -- main code for gopl.io/ch7/surface --

//!+parseAndCheck
func parseAndCheck(s string) (eval.Expr, error) {
    if s == "" {
        return nil, fmt.Errorf("empty expression")
    }
    expr, err := eval.Parse(s)
    if err != nil {
        return nil, err
    }
    vars := make(map[eval.Var]bool)
    if err := expr.Check(vars); err != nil {
        return nil, err
    }
    for v := range vars {
        if v != "x" && v != "y" && v != "r" {
            return nil, fmt.Errorf("undefined variable: %s", v)
        }
    }
    return expr, nil
}

//!-parseAndCheck

//!+plot
func plot(w http.ResponseWriter, r *http.Request) {
    r.ParseForm()
    expr, err := parseAndCheck(r.Form.Get("expr"))
    if err != nil {
        http.Error(w, "bad expr: "+err.Error(), http.StatusBadRequest)
        return
    }
    w.Header().Set("Content-Type", "image/svg+xml")
    surface(w, func(x, y float64) float64 {
        r := math.Hypot(x, y) // distance from (0,0)
        return expr.Eval(eval.Env{"x": x, "y": y, "r": r})
    })
}

//!-plot

//!+main
func main() {
    http.HandleFunc("/plot", plot)
    log.Fatal(http.ListenAndServe("localhost:8000", nil))
}

//!-main