I want to make a plot like that using R:

![orthographic projection](https://i.stack.imgur.com/8PePQ.png)

All I want is the country borders as seen from outer space, no fancy colors needed. It seems I need to use the `spTransform` function, but it gives me a "non finite transformation detected" error. I've been told that I need to apply a [cosine formula](http://en.wikipedia.org/wiki/Orthographic_projection_in_cartography#Mathematics) to each point in my world shapefile, and erase those that goes behind the Earth. This has 2 problems:

1. It looks like something the algorithm should do automatically;
2. I cannot just erase the points behind the Earth, cause this would destroy the topology of the polygons.

Isn't it a simple task? How should I do it?

EDIT - What I've done so far:

The shapefile was downloaded from [here](http://thematicmapping.org/downloads/TM_WORLD_BORDERS-0.3.zip) to a folder named "shp". The R code is just:

```
library(rgdal)
countries <- readOGR("shp","TM_WORLD_BORDERS-0.3",encoding="UTF-8",stringsAsFactors=F)
countries <- spTransform(countries,CRS("+proj=ortho +lat_0=-10 +lon_0=-60"))

```

It gives me the error

```
non finite transformation detected:
[1] 45.08332 39.76804      Inf      Inf
Erro em .spTransform_Polygon(input[[i]], to_args = to_args, from_args = from_args,  : 
  failure in Polygons 3 Polygon 1 points 1
Além disso: Mensagens de aviso perdidas:
In .spTransform_Polygon(input[[i]], to_args = to_args, from_args = from_args,  :
  108 projected point(s) not finite

```