I find tabix to be much easier / much sorter command line arguments.

You don't need a fasta for this method. Tabix is screaming fast.

bgzip your.vcf
tabix -p vcf your.vcf
tabix your.vcf.gz chr1:10,000,000-20,000,000

For others if you like to use BED files, one way to do this would be like so:

vcftools --vcf input.vcf --bed bed_file_describing_the_range.bed --out output_prefix --recode --keep-INFO-all

Where bed_file_describing_the_range.bed has the positions of interest.

bedtools intersect worked better to me

intersectBed -a input.vcf -b /path/to/my.interval.bed -header > output.vcf

Another straightforward option would be with bcftools: https://samtools.github.io/bcftools/bcftools.html#view

As a general example like this: bcftools view -R yourRegionFile -o outFile yourVCFfile

Interestingly the region file "yourRegionFile" can be specified either on command line or in a VCF, BED, or tab-delimited file (the default). See the bcftools manual for regions file here: https://samtools.github.io/bcftools/bcftools.html#common_options

bcftools view -R regions.bed your.vcf > output.regions.vcf

You could use the GATK SelectVariants Walker, specifying the -L option to set the intervals your are interested in.

Here is an example of how to do that, taken from the link above:

#Select a sample and restrict the output vcf to a set of intervals:     
java -Xmx2g -jar GenomeAnalysisTK.jar \
       -R ref.fasta \
       -T SelectVariants \
       --variant input.vcf \
       -o output.vcf \
       -L /path/to/my.interval_list \
       -sn SAMPLE_1_ACTG

Note that you have to have a fasta reference file with the same names and coordinates as you use in our region file and vcf, and that you can remove the -sn option if you want to extract the variations for all samples.

Hope this helps.

I did something like what you describe, but to create multiple VCF files. Uses bedtools:

bedtools intersect worked better to me

intersectBed -a input.vcf -b /path/to/my.interval.bed -header > output.vcf