---
title: "Plotting tri-objective models"
author: "Lars Relund Nielsen"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Plotting tri-objective models}
  %\VignetteEncoding{UTF-8}
  %\VignetteEngine{knitr::rmarkdown}
editor_options: 
  chunk_output_type: console
---

```{r setup, include = FALSE}
library(knitr)
library(rgl)
library(ggsci)
library(magrittr)
rgl::setupKnitr()
options(rgl.useNULL=TRUE)
rgl::par3d("family" = "serif")
opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  warning=FALSE, message=FALSE, include = TRUE, 
  out.width = "99%", fig.width = 8, fig.align = "center", fig.asp = 0.62
)

if (!requireNamespace("rmarkdown", quietly = TRUE) || !rmarkdown::pandoc_available("1.14")) {
   warning(call. = FALSE, "These vignettes assume rmarkdown and pandoc version 1.14 (or higher). These were not found. Older versions will not work.")
   knitr::knit_exit()
}
```

With `gMOIP` you can make plots of the criterion space for tri-objective models (linear
programming (LP), integer linear programming (ILP), or mixed integer linear programming (MILP)).
This vignette gives examples on how to make plots of the criterion space.

First we load the package:

```{r, cache=FALSE}
library(gMOIP)
```

The criterion space can be plotted for tri-objective models. An example with many unsupported:

```{r, webgl=TRUE, cache=FALSE}
view <- matrix( c(0.333316594362259, 0.938472270965576, -0.0903875231742859, 0, 0.83994072675705, -0.339126199483871, -0.423665106296539, 0, -0.428250730037689, 0.0652943551540375, -0.901297807693481, 0, 0, 0, 0, 1), nc = 4)
loadView(v = view)
set.seed(1234)
pts <- genNDSet(3, 100, argsSphere = list(below = FALSE), dubND = FALSE)
pts <- classifyNDSet(pts[,1:3])
head(pts)
ini3D(argsPlot3d = list(xlim = c(min(pts[,1])-2,max(pts[,1])+2),
   ylim = c(min(pts[,2])-2,max(pts[,2])+2),
   zlim = c(min(pts[,3])-2,max(pts[,3])+2)))
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))
plotPoints3D(pts[!pts$sne,1:3], argsPlot3d = list(col = "black"))
plotPoints3D(pts[!pts$us,1:3], argsPlot3d = list(col = "blue"))
plotCones3D(pts[,1:3], rectangle = TRUE, argsPolygon3d = list(alpha = 1, color = "cornflowerblue"))
plotHull3D(pts[,1:3], addRays = TRUE, argsPolygon3d = list(alpha = 0.25, color = "red"), useRGLBBox = TRUE)
finalize3D(argsAxes3d = list(edges = "bbox"))
```

Example with many supported:

```{r, webgl=TRUE, cache=FALSE}
loadView(v = view)
pts <- genNDSet(3, 50, argsSphere = list(below = TRUE), dubND = FALSE)
pts <- classifyNDSet(pts[,1:3])
ini3D(argsPlot3d = list(xlim = c(min(pts[,1])-2,max(pts[,1])+2),
   ylim = c(min(pts[,2])-2,max(pts[,2])+2),
   zlim = c(min(pts[,3])-2,max(pts[,3])+2)))
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))
plotPoints3D(pts[!pts$sne,1:3], argsPlot3d = list(col = "black"))
plotPoints3D(pts[!pts$us,1:3], argsPlot3d = list(col = "blue"))
plotCones3D(pts[,1:3], rectangle = TRUE, argsPolygon3d = list(alpha = 1, color = "cornflowerblue"))
plotHull3D(pts[,1:3], addRays = TRUE, argsPolygon3d = list(alpha = 0.25, color = "red"), useRGLBBox = TRUE)
finalize3D(argsAxes3d = list(edges = "bbox"))
```

## Classifying

Non-dominated points can be classified using `classifyNDSet`:

```{r}
pts <- matrix(c(0,0,1, 0,1,0, 1,0,0, 0.5,0.2,0.5, 0.25,0.5,0.25), ncol = 3, byrow = TRUE)
open3d()
ini3D(argsPlot3d = list(xlim = c(min(pts[,1])-2,max(pts[,1])+2),
  ylim = c(min(pts[,2])-2,max(pts[,2])+2),
  zlim = c(min(pts[,3])-2,max(pts[,3])+2)))
plotHull3D(pts, addRays = TRUE, argsPolygon3d = list(alpha = 0.5), useRGLBBox = TRUE)
pts <- classifyNDSet(pts[,1:3])
pts
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))
plotPoints3D(pts[!pts$sne,1:3], argsPlot3d = list(col = "black"))
plotPoints3D(pts[!pts$us,1:3], argsPlot3d = list(col = "blue"))
plotCones3D(pts[,1:3], rectangle = TRUE, argsPolygon3d = list(alpha = 1))
finalize3D()
rglwidget(reuse = F)
```


```{r}
pts <- genNDSet(3,50, dubND = FALSE)[,1:3]
open3d()
ini3D(argsPlot3d = list(xlim = c(0,max(pts$z1)+2),
  ylim = c(0,max(pts$z2)+2),
  zlim = c(0,max(pts$z3)+2)))
plotHull3D(pts, addRays = TRUE, argsPolygon3d = list(alpha = 0.5))
pts <- classifyNDSet(pts[,1:3])
pts
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))
plotPoints3D(pts[!pts$sne,1:3], argsPlot3d = list(col = "black"))
plotPoints3D(pts[!pts$us,1:3], argsPlot3d = list(col = "blue"))
finalize3D()
rglwidget(reuse = F)
```

The classification is done using the `qhull` algorithm that find the convex hull of the points including the rays. If a vertex then if must be supported extreme. Next we use the `inHull` algorithm to find out if the remaining are on the border or not (supported non-extreme and unsupported). 

```{r, include=F}
rm(list = ls(all.names = TRUE))
```



